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In this paper, by taking the NLS-type equations as examples, we propose a novel high-order explicit energy-preserving Lie-group method for Hamiltonian PDEs. The main idea is to combine recently developed generalized SAV (G-SAV) approach (Cheng et al., 2021) and explicit Lie group method, in which the fourth-order or higher-order Lie group method only composes two exponentials in each stage, and this is the key point that the proposed methods can preserve energy of Hamiltonian PDEs. This is our first attempt to construct high-order explicit energy-preserving methods without using projection technique (Hairer et al., 2006 [14]), and some stability conclusions of our proposed methods for the NLS-type equations are also presented. Finally, we present 2D and 3D numerical simulations to demonstrate the stability and accuracy. [ABSTRACT FROM AUTHOR]

In this paper, our main objective is to build fuzzy upwind difference scheme for fuzzy convection–diffusion equations based on generalized Hukuhara derivative with new Taylor expansions. The truncation error and consistency of this scheme are discussed in the sequel. Stability of this scheme is proved by fuzzy Fourier transform, and convergence of this scheme is derived by Lax equivalence theorem. Finally, a numerical example is given and shows that our methods are efficient and stable for solving fuzzy convection–diffusion problems. [ABSTRACT FROM AUTHOR]

Climate change is driven by the increase in greenhouse gases in Earth's atmosphere, especially carbon dioxide (CO 2), leading to a rise in the global average temperature. This temperature rise unleash far-reaching and profound consequences on various living organisms. In this research work, we formulate a nonlinear mathematical model to perceive the impact of rising temperature on wildlife species. In formulating the model, we take into account that the escalating CO 2 concentration contributes to a rise in the global average temperature, thereby impacting the growth rate of wildlife population. We pinpoint the sufficient conditions for all the dynamic variables to reach their simultaneous equilibrium levels. The model analysis reveals a spectrum of bifurcations, including transcritical, Hopf, saddle–node, and Bogdanov–Takens bifurcations. Further, the examination of transcritical bifurcation led to the identification of a critical reduction rate of wildlife species due to human activities above which the wildlife population may teeter on the brink of extinction under the considered stressor of temperature rise. This extinction of wildlife species can be avoided by increasing the carrying capacity of forest biomass. Also, we have shown that for a specific set of parameter values, there exists a bistability between the forest-wildlife free equilibrium and the coexisting equilibrium. [ABSTRACT FROM AUTHOR]

The paper presents a class of predator–prey model with density-dependent diffusion in the spatially heterogeneous environment. We first provide the global existence and boundedness of the solution for the model. Then, by taking a variable transformation, the difficulty brought by the cross-diffusion can be overcome, and the existence, stability and local bifurcation of semi-trivial steady-state solutions for the equivalent system are further studied. Finally, the existence of positive solutions of the system is also given by using the Leray–Schauder degree theory and the method of principle eigenvalue, especially for the limit cases when the diffusion coefficient tends to zero or infinite. [ABSTRACT FROM AUTHOR]

This paper analyzes a discrete-time Cournot competition model with time delays taking into consideration the dynamics of market interactions involving one public firm and multiple private firms. The model assumes that the production output of the public firm is influenced by the past output levels of the private firms. The output levels of the private firms are affected by the past production outputs of both the public firm and their private competitors. The study identifies two equilibrium states within the nonlinear system: a positive equilibrium and a boundary equilibrium. Through a stability analysis, it is established that the boundary equilibrium is a saddle point. In the absence of time delays, the stability region for the positive equilibrium is determined. The research explores various specific delay scenarios, finding conditions under which the positive equilibrium is asymptotic stability. Additionally, the occurrence of flip and Neimark–Sacker bifurcations are examined. In order to illustrate the complex dynamics, the paper provides a series of numerical examples. • We explore Cournot competition with delays, involving both public and private firms. • Two equilibria are found: positive and boundary, with boundary as a saddle point. • Stability of positive equilibrium is analyzed, with and without time delays. • Flip/Neimark–Sacker bifurcations are investigated supported by numerical examples. [ABSTRACT FROM AUTHOR]

We propose a modification of multistep collocation methods for Volterra integro-differential equations, an important type of Volterra equations including the derivative and integral of the unknown solution. Superimplicit interpolations are employed to represent the collocation polynomial. The investigation on the existence and convergence of the collocation solution shows that the proposed approach is able to attain a high convergence rate without adding collocation points. Besides, the stability analysis of the proposed collocation method indicates that its stability region can be enlarged by adjusting interpolation nodes. Several numerical experiments are provided to confirm theoretical results. [ABSTRACT FROM AUTHOR]

Ginger has traditionally been used to treat and prevent nausea and vomiting; however, the results of clinical trials are ambiguous. The efficacy of ginger is attributed to gingerols and their metabolites, shogaols. Since these compounds have different pharmacological profiles, the clinical efficacy of ginger products is largely dependent on their chemical composition. The goal of our study was to examine the stability of ginger, determining the 6-gingerol contents in order to assess the effects of different storage conditions. We have performed a 6-month stability test with dry ginger rhizome samples stored in a constant climate chamber in three different storage containers (uncovered glass container, glass container sealed with rubber stopper, and plastic container). The 6-gingerol contents were measured by HPLC method. The concentration of 6-gingerol decreased in all samples. In the sealed glass container, the decrease in 6-gingerol content was significantly lower than in the unsealed glass container and in the plastic container. These results demonstrate that storage conditions have a significant impact on the quality of ginger, which may also affect efficacy. [ABSTRACT FROM AUTHOR]

For delay patch-constructed periodic Nicholson's blowflies system, the global stability on positive periodic solutions remains imperfectly understood at best. In this paper, by combining the fluctuation lemma with elementary inequality techniques, we build up several novel criteria to ensure the global asymptotic stability of positive periodic solutions of the proposed model, which have essentially novelty and supplement some existing literature. In particular, we afford some numerical simulations to substantiate the validness and efficacy of the obtained theoretic results. [ABSTRACT FROM AUTHOR]

This research intends to determine the influence of granulated cork on the physical, thermal and mechanical properties of the concrete block. Absorption, density, moisture content, compressive strength and thermal conductivity tests were carried out on concrete blocks produced in a traditional way, with a substitution of sand by granulated cork at 3 % and 5 % in two experimental groups, in addition to one standard group. In the case of the physical properties, absorption presented average values of 9.47 %, 8.23 %, and 9.37 % for the standard group (BP) and experimental groups (BC3 and BC5) respectively. Density values showed an increase as the percentage of cork grew, reaching a density of 2088.77 kg/m3 for the group with 5 % cork. Respecting moisture content, its values decreased from 13.67 % for BP, 11.87 % for BC3, and finally 9.23 % for BC5. The mechanical property of compressive strength showed variations of increase and decrease with values of 19.53 kg/cm² for the BP group, 23.10 kg/cm² for the BC3 group, and 16.21 kg/cm² for the BC5 group. Lastly, for the thermal conductivity test, the results decreased as expected with values of 0.387 W/mK, 0.3164 W/mK, and 0.3036 W/mK for the BP, BC3 and BC5 groups respectively. These data processed with statistical tests showed that the incorporation of granulated cork in the concrete block has a significant influence on its physical, thermal and mechanical properties. [ABSTRACT FROM AUTHOR]

• Ultrahigh energy storage performances were presented in BBTMT- x ceramics. • ESPs possess outstanding temperature, frequency and cycling stability. • The relationship between structures and enhanced ESPs was established. • Experimental results were supported well by FEM analysis results. • The materials have great potential for advanced pulse power capacitor applications. (Ba (1– x) Bi x)(Ti (1– x) Mg 2 x /3 Ta x /3)O 3 (BBTMT- x, x = 0.075, 0.1, 0.125, and 0.15) ceramics were manufactured via a solid-phase reaction method. The pseudo-cubic BaTiO 3 (BT) as the primary phase and Ba 4 MgTi 11 O 27 as the secondary phase were detected in BBTMT- x ceramics. The elongated rod-shaped grains therein became numerous as x increased. The introduction of Bi/Mg/Ta (BMT) elements transformed BT ceramics from ferroelectrics to relaxor ferroelectrics and induced the formation of short-range order polar nanoregions (PNRs), which were beneficial for the preeminent energy storage properties (ESPs). The highest ESPs (a giant recoverable energy-storage density W rec of 5.97 J cm–3 with a high-efficiency η of 87.4%) were achieved in BBTMT-0.1 ceramics at 710 kV cm–1. BBTMT-0.1 ceramics also possessed excellent frequency (1–500 Hz), temperature (30–150 °C), and fatigue (cycle number of 1–100,000) stabilities. Finite element simulations (FES) demonstrated that elongated rod-shaped grains had stronger obstacles to the development of electrical branches, which was beneficial to improving the comprehensive ESPs. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper proposes a novel L1-based predictor–corrector method for the fractional differential equations involving generalized-Caputo type derivative. A decomposition scheme is used to obtain the three-point predictor–corrector formula. The error and stability of the proposed method are given in detail. A computer virus and a five-dimensional Hopfield neural network models are solved using the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, considering the spatial propagation behavior of Internet rumor, we propose a new reaction–diffusion rumor propagation model with time delay in social networks. Based on this, we discuss the stability conditions at the equilibrium point and analyze the Turing instability for the approximation propagation system. Simultaneously, the amplitude equations for the approximation system are derived by multiscale analysis. We use numerical simulation to compare the effect of parameter size, period, and time delay on the patterns. Moreover, we compare the different reactivity of the system in the W S networks and the B A networks. Finally, we plot the corresponding amplitude equations patterns by controlling the parameters and verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

The main challenge in kernel-based approximation theory and its applications is the conflict between accuracy and stability. Hybrid kernels can be used as one of the simplest and most effective tools to manage this challenge. This article uses a meshless scheme based on hybrid radial kernels (HRKs) to solve second kind Fredholm integral equations (FIEs). The method estimates the solution via the discrete collocation procedure based on a hybrid kernel that combines appropriate kernels with suitable weight parameters. The optimal parameters in the hybrid kernels can be calculated using the particle swarm optimization (PSO) algorithm based on the root mean square (RMS) error. This technique converts the problem under investigation into a system of linear equations. Moreover, the convergence of the suggested hybrid approach is studied. Lastly, some numerical experiments are included to reveal the accuracy and stability of the hybrid kernels approach. The numerical results demonstrate that the presented hybrid procedure meaningfully reduces the ill-conditioning of the operational matrices, at the same time, it maintains the accuracy and stability for all values of shape parameters. [ABSTRACT FROM AUTHOR]

This paper aims to obtain the numerical solution of a one-dimension fourth-order Kuramoto-Sivashinsky (KS) equation, which has application in the context of flame propagation. This study combines the implementation of two new mechanisms quintic Uniform Algebraic Hyperbolic (QUAH) tension B-spline and quintic Uniform Algebraic Trigonometric (QUAT) tension B-spline with a renowned method known as Differential Quadrature Method (DQM). DQM is used to approximate the derivatives. Then, to obtain the weighting coefficients both quintic splines QUAH and QUAT are implemented with DQM and the original boundary value problem was then transformed into an ordinary differential equation. The Runge-Kutta 43 technique was used to solve the resultant ODE. With this approach, the outcomes are precise and close to the exact solution. The differential quadrature technique has a significant advantage over the previous approaches because it prevents the perturbation in order to find the better results for the given nonlinear equations. The accuracy of the suggested method is then illustrated numerically resolving four test problems and calculating the error norms L 2 and L ∞. Calculated results are displayed graphically and in tabular format for quick and simple access. This paper introduces an original work, to the best of the author's knowledge. The obtained solution and graphical observations show that QUAH and QUAT tension B-splines with DQM is a strong and dependable methods for estimating nonlinear problem solutions. Quintic B-splines are higher-order interpolation method compared to lower-degree B-splines, which results in more accurate approximations, and provides smooth and continuous representations of functions. Moreover, DQM when combined with quintic B-splines, can help reduce numerical dispersion, and can be applied to a wide range of problems. • Two new regimes of order six, referred as Uniform Algebraic Trigonometric and Uniform Algebraic Hyperbolic are proposed. • The Kuromoto-Sivashinsky equation (KS) is numerically solved by combining DQM with splines. • Four test problems have been resolved to gauge how well the current approach works. • Error norms and convergence order are calculated to evaluate the precision and efficiency of the approach. • The unconditional stability of the suggested technique has been proved. [ABSTRACT FROM AUTHOR]

In this paper, a linearized numerical scheme of nonlinear variable-order fractional diffusion equation with time delay is constructed. We apply the L 2 − 1 σ formula to discretize the temporal derivative and second-order central difference scheme to discretize the spatial derivative. The proposed method is unconditionally stable and convergent with O τ 2 + h 2 , where τ and h are the time and space steps, respectively. Numerical experiment demonstrates the effectiveness and accuracy of the numerical scheme. [ABSTRACT FROM AUTHOR]

The dissemination of public health information through television and social media posts is essential for informing the public about the transmission of contagious diseases, which is crucial in preventing the spread of various infectious diseases. In this paper, we propose a non-linear mathematical model to assess the effect of advertisements through social media in creating awareness and limiting treatment on spreading infectious diseases. These initiatives may alter population behaviour and divide the susceptible population into subgroups. In addition, to comprehend these dynamics better, we use half-saturation constant rates for media coverage and treatment. The model's well-posedness and feasibility are evaluated. The possible biological equilibrium points are calculated. Local and global stability are carried out. The objective of our study is to produce the model's bifurcation. Transcritical, Saddle–node, Hopf bifurcation of codimension 1 and Cusp, Generalized-Hopf (Bautin), and Bogdanov–Takens (BT) bifurcation of codimension 2 are studied for this purpose. Due to the limited medical resources and supply efficiency, the model exhibits backward bifurcation, resulting in bistability. Moreover, the occurrence condition for stability and direction of Hopf bifurcation is discussed. This model study demonstrates that the system is significantly influenced by the pace with which awareness programmes are implemented and that raising this value above a threshold may result in continuous oscillation. Sensitivity analysis employs the normalized forward sensitivity index of the basic reproduction number to provide a comprehensive understanding of the effect of various parameters on accelerating and limiting disease spread. Further, the minimum possible cost is determined by formulating an optimal control system based on sensitivity analysis and applying Pontryagin's maximum principle. Methods of cost-effectiveness, such as ACER and ICER, are used to determine the most cost-effective control intervention strategy among all the strategies. Numerical simulations have been done to support all theoretical findings. • A non-linear model is proposed to assess the effect of advertisements through social media and limiting treatment on infectious diseases. • Due to backward bifurcation, R 0 ¡ 1 is insufficient to eliminate the sickness, and additionally, the model displays Hopf, Saddle–node, Bogdanov–Takens, and Generalized Hopf bifurcation. • Strategies having the highest infection-averted capacity using treatment and media implementation as control parameters are obtained. • Different control techniques are compared using numerical simulation, and sensitivity analysis is used to determine the appropriate control parameter. • Using method like ACER and ICER, we determine the most cost-effective strategy. [ABSTRACT FROM AUTHOR]

This research introduces the fractional non-polynomial spline method as a novel scheme for solving the time-fractional Korteweg-de Vries (KdV) equation. The study focuses on numerical analysis and algorithm development for simulation purposes. The proposed method involves the construction of a fractional non-polynomial spline to estimate the equation's solution, offering improved precision and modeling capabilities compared to existing approaches. To assess the stability of the proposed approach, the von Neumann method is employed, demonstrating its unconditional stability within a specific parameter range. To validate the effectiveness of our numerical analysis and simulation algorithm, contour, 2D, and 3D graphs are utilized to compare the solution obtained through our method with an analytical solution. Through rigorous comparative analysis with previous works, the superiority of our approach in terms of accuracy and efficiency is demonstrated. Norm error calculations, specifically the ( L 2 and L ∞) error norms, provide a quantitative assessment of the accuracy and reliability of our proposed scheme. [ABSTRACT FROM AUTHOR]

In natural ecosystems, predators often live in groups and have evolved cooperative hunting behaviors over time. This cooperative behavior on the one hand increases the success rate of the prey, but it also leads to the fear response of prey to predators, thereby affecting the reproduction rate of prey populations. In the current study, we put forward a fishery model for renewable aquatic resource with dual effects of fear and cooperative hunting, and investigate the impact of fear level and cooperative hunting intensity on the dynamics of the model. The analysis shows that the level of fear and the intensity of cooperative hunting can affect the existence and number of coexisting equilibria. Secondly, from the perspective of rational exploitation of fishery resources, we adopt a state-feedback intermittent fishing strategy, which fully considers the current status of the target species and avoids the impact of irrational fishing on the ecosystem. We investigate the dynamic behavior of the fishery model under discontinuous fishing model, including the existence and stability of predator-extinction periodic solution and co-existence order-1 and order-2 periodic solutions under different fishing thresholds, which not only provides a possibility to fishing species according to the period, but also ensures a certain robustness of the fishing strategy. Finally, the main results are verified by numerical simulations using MATLAB program and their biological implications are discussed. [ABSTRACT FROM AUTHOR]

• Design strategy for efficient and durable electrocatalyst by introducing local interface strain are proposed. • The elaborately designed Ir@NiO/C BDC catalyst displays outstanding alkaline overall water splitting stability with 1800 h at 10 mA/cm2. • The outstanding electrochemical performance of all pH range ensures the driving of water splitting reaction under universal conditions. • The excellent structural stability arising from its increased the Ir and Ni vacancy formation energies achieved by introduced interfacial strain. Strain engineering of two-dimensional (2D) material interfaces represents a powerful strategy for enhancing the electrocatalytic activity of water splitting. However, maintaining catalytic stability under various harsh conditions by introducing interface strain remains a great challenge. The catalyst developed and evaluated herein comprised Ir clusters dispersed on 2D NiO nanosheets (NSs) derived from metal organic frameworks (Ir@NiO/C BDC), which displays a high activity and stability under all pH conditions, and even a change of only 1% in the applied voltage is observed after continuous electrocatalytic operation for over 1800 h under alkaline conditions. Through combined experimental and computational studies, we found that the introduced interfacial strain contributes to the outstanding structural stability of the Ir@NiO/C BDC catalyst, arising from its increased Ir and Ni vacancy formation energies, and hence suppressing its leaching. Moreover, strain also enhances the kinetically sluggish electrocatalytic water splitting reaction by optimizing its electronic structure and coordination environment. This work highlights the effects of strain on catalyst stability and provides new insights for designing widely applicable electrocatalysts. [Display omitted] [ABSTRACT FROM AUTHOR]

• The demetallation process (fast decay) is immune to the pressure and temperature fluctuations. • The "slow decay" is significantly dependent on the different operating conditions. • The evolution from Fe-N to Fe-O bonds could be the root-cause of the "slow decay" after demetallation. The state-of-the-art Fe/N/C catalyst has presented comparable initial cathode performance to the benchmark Pt/C catalyst in proton exchange membrane fuel cells (PEMFCs). However, the major bottleneck is its significant activity decay in real-world PEMFC cells. The superposed "fast decay" and "slow decay" have been well documented to describe the degradation process of Fe/N/C catalysts during PEMFC operation. The fast decay has been well understood in close relation to the demetallation at the initial 15-h stability test. Nevertheless, it is still unclear how the remanent active sites evolve after demetallation. To this end, the catalyst performance and evolution of a typical Fe/N/C active site were herein investigated through postmortem characterizations of the membrane electrode assemblies (MEAs) after different operations. It is presented that 1 bar pressure and 80 °C temperature are the optimized conditions for Fe/N/C MEA. Particularly, the "fast decay" in the initial 15 h is immune to the various operating parameters, while the "slow decay" highly depends on the applied temperature and pressure. According to the X-ray absorption spectra (XAS) analysis and stability test of MEA, the gradual evolution of Fe-N coordination to Fe-O is found correlated with the "slow decay" and accounts for the catalyst decay after the demetallation process. [Display omitted] [ABSTRACT FROM AUTHOR]

An age-structured SVIR epidemic model with different compartment ages and two delays is investigated. The model is transformed into a non-densely defined abstract Cauchy problem. The basic properties, including the positivity and boundedness of solutions, basic reproduction number R 0 and the existence of equilibria, are first derived. The linearized system and characteristic equation at an equilibrium from the corresponding abstract Cauchy problem are also obtained. When R 0 < 1 , the local stability of the disease-free equilibrium is proved, and when R 0 > 1 and the two delays vanish, the local stability of the endemic equilibrium is proved. When R 0 > 1 , and Assumptions 1 and 2 are satisfied, the existence of Hopf bifurcation are established respectively in the general case with two delays as bifurcation parameters and in three special cases with only one delay as the bifurcation parameter. The results show that disease with the incubation period and the infection period of infection age has very complex dynamical behavior at the endemic equilibrium. Finally, numerical examples validate the theoretical results. [ABSTRACT FROM AUTHOR]

The objective of this study is to determine the influence of the addition of calcined potato peel on the physical and mechanical properties of hot asphalt mixes - Huánuco, 2023. Regarding the methodology, a quantitative, applied and experimental design study is used, applying the observation and the recording sheet in a sample of 45 briquettes with additions of 2.0 %, 4.0 %, 6.0 % and 8.0 % of calcined potato peel, compared with a standard sample containing 2.0 % hydrated lime, where They evaluate properties such as void content, flow resistance and stability. The results show that the best air content was 3.3 % and flow resistance was 3.4 mm, which was achieved with 2.0 % addition of calcined potato peel; However, the highest stability was obtained with 4.0 % addition, the value being 1,272.3 kg. It is concluded that, with an addition of 2.0 %, the best physical and mechanical properties of the asphalt mixtures are achieved; However, no significant variations were evident in the ANOVA test for flow resistance and stability (p > 0.05). [ABSTRACT FROM AUTHOR]

Cannabis as a therapeutic agent is increasing in popularity all around the globe, particularly in Western countries, and its potential is now well assessed. On the other hand, each country has its own regulation for the preparation of cannabis macerated oils; in Italy, there are only a few preparation methods allowed. With this work, we aim to perform a stability study of cannabis oils produced with a novel method for the extraction of cannabinoids from cannabis inflorescence. Three different varieties of cannabis were used, with and without the adding of tocopherol acetate as an antioxidant. Cannabinoids were extracted using ethanol at room temperature; then, the solvent was evaporated under reduced pressure and the preparations reconstituted with olive oil. In this work, we assessed the stability of both cannabinoids and terpenes in these formulas over 8 months. Cannabinoid stability was assessed by monitoring the concentrations of THC and CBD, while terpene stability was assessed by monitoring β -Caryophyllene and α -Humulene concentrations. Stability of the extracts was not influenced by the presence of tocopherol acetate, though refrigeration seems to be detrimental for a long storage of products, especially regarding THC concentrations. The improvements offered by this method reside in the flexibility in controlling the concentration of the extract and the ability to produce highly concentrated oils, alongside the possibility to produce standardized oils despite the variability of the starting plant material. [ABSTRACT FROM AUTHOR]

We present a dynamic output feedback fuzzy model predictive control (FMPC) approach for the Takagi–Sugeno model with bounded disturbance in this paper. The proposed approach relies on the formulation, at each sampling instant, of a lexicographic optimization problem that takes into account multiple objectives including improving the control performance, enlarging the region of attraction (ROA) and tightening the estimation error set (EES). Since the controller parameters and Lyapunov matrices are kept as degrees of freedom for the lower-ordered optimization problems, larger ROA and less conservative EES are obtained. As a result, the control performance can be greatly improved with respect to previous works. Furthermore, we prove the recursive feasibility of the approach and guarantee the stability of the closed-loop system. The result is verified through a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we explore relationships among the pairs of various well-known contractive type operators in Banach spaces. We also present a novel Jungck type iteration algorithm for a pair of quasi-contractive operators, which is thoroughly investigated in terms of strong convergence, stability, and data dependency. To demonstrate the efficacy of the proposed algorithm and reliability of each of the mentioned results, we furnish illustrative academic examples including both linear and nonlinear DEs. Furthermore, we present several open problems that warrant further study. Our results complement recent findings in the literature and contribute to further development in this area. [ABSTRACT FROM AUTHOR]

A higher-order finite difference method is developed to solve the variable coefficients convection–diffusion singularly perturbed problems (SPPs) involving fractional-order time derivative with the order α ∈ (0 , 1). The solution to this problem class possesses a typical weak singularity at the initial time t = 0 and an exponential boundary layer at the right lateral surface as the perturbation parameter ɛ → 0. Alikhanov's L 2 − 1 σ approximation is applied in the temporal direction on a suitable graded mesh, and the spatial variable is discretized on a piecewise uniform Shishkin mesh using a combination of midpoint upwind and central finite difference operators. Stability estimates and the convergence analysis of the fully discrete scheme are provided. It is shown that the fully discrete scheme is uniformly convergent with a rate of O (M − p + N − 2 (log N) 2) , where p = min { 2 , r α } , r is the graded mesh parameter and M , N are the number of mesh points in the time and space direction, respectively. Two numerical examples are taken in counter to confirm the sharpness of the theoretical estimates. • The proposed scheme uses the Alikhanov's L 2 − 1 σ approximation to discretize the Caputo's time fractional derivative on a suitably designed graded mesh with exponent r in the temporal direction. • Further, a combination of midpoint upwind and central difference operators are used on a piecewise uniform mesh to discretize the spatial variable. To meet the required monotonicity constraints, we use the central difference operator in the finer mesh region and the midpoint upwind technique in the coarse mesh region. • It is shown that the fully discrete scheme is uniformly convergent with a rate of O (M − p + N − 2 (l o g N) 2) , where p = min { 2 , r α } , M , N are the number of mesh points in the time and space direction, respectively. • Two numerical examples are taken in counter to confirm the sharpness of the theoretical estimates. • The primary feature of the suggested approach is that it is stable, generates high-order accurate numerical results and effectively captures the initial and boundary layers behaviors due to the concentration of mesh points in the neighborhood of layer regions. [ABSTRACT FROM AUTHOR]

• We present cesium formate as a versatile chemical additive that serves to both passivate defects in perovskite solar cells and improve roll-to-roll processability. • The cesium and formate ions successfully passivate surface defects by facilitating robust interactions between the molecules and perovskite components. • Incorporating the chemical additive leads to enhanced crystalline properties in roll-to-roll processed perovskite solar cells, resulting in a power conversion efficiency exceeding 14%. Organic–inorganic halide perovskites have significant potential for application in next-generation solar cells. However, their applications are limited by challenges associated with large-area processability and long-term stability owing to the presence of pinholes and defect sites. Here, we incorporated cesium formate in a perovskite active layer using a sequential perovskite fabrication process to eliminate the defect sites of perovskites and improve the film processability via roll-to-roll (R2R) processing. The addition of cesium formate salt to the PbI 2 layer influences the perovskite crystal formation behavior as well as increases the perovskite crystallinity and decreases the defect density. Furthermore, cesium formate addition eliminated small PbI 2 grains and smoothed the perovskite surface, resulting in a large crystal grain size. The formate ions interact with the PbI 2 component and passivate halide vacancy defects, reducing nonradiative recombination and improving charge transfer. Additionally, the treated perovskite films were highly stable in air, exhibiting improved efficiency retention over time and achieving a power conversion efficiency (PCE) of > 22% compared to the control. Furthermore, the additive-treated perovskite film was processed using the R2R method, achieving a high PCE of >14% with minimal hysteresis. [Display omitted] [ABSTRACT FROM AUTHOR]

• A simple yet efficient strategy for long term storage of MXene suspension by introducing glycerol, a typical polyhydric alcohol, was developed. • The effectiveness of the strategy is evidenced by structural compositional and morphological investigations. • Glycerol protects the defective sites of MXene flakes through restricting water and/or oxygen molecules from reactive sites. • The strategy based on polyhydric alcohols has the potential to be extended to other MXenes, solving the most urgent challenge in the field of MXene engineering. MXenes have promises in myriad applications by virtue of two-dimensional nature and adjustable functional groups. To achieve the applications, MXenes are always first prepared in the form of aqueous suspension. However, fast degradation caused by the attack of dissolved oxygen and water molecules is the main obstacle to the application of MXenes. It has come to light that the degradation preferentially takes place at defective sites and edges where defects enrich. To tackle this problem and increase the stability, herein, using Ti 3 C 2 T x MXene as a model material, we report a simple yet efficient strategy for long term storage of MXene suspension by introducing glycerol, a typical polyhydric alcohol. The effectiveness of the strategy is evidenced by structural compositional and morphological investigations. Glycerol protects the defective sites of MXene flakes through restricting water and/or oxygen molecules from reactive sites. This is supported by ab initio molecular dynamics simulations that form hydrogen bonds between MXene and glycerol molecules just over defective sites. Following this mechanism, other polyhydric alcohols, such as ethylene glycol and propylene glycol, are also effective in stabilizing Ti 3 C 2 T x MXene suspension. The strategy based on polyhydric alcohols has the potential to be extended to other MXenes, solving the most urgent challenge in the field of MXene engineering. [Display omitted] [ABSTRACT FROM AUTHOR]

Designing an efficient high-order numerical discretization is one of the challenges in numerical solution of fractional differential equations. Therefore in this paper to overcome the ill-conditioning that often destroys the convergence rate of global RBF methods, we apply a local meshfree method known as radial basis function-generated finite difference (RBF-FD) method equipped with a greedy algorithm to design stable stencil weights and approximate spatial derivatives for parabolic fractional partial differential equations (FPDEs) of convection–diffusion–reaction type. In RBF-FD method to select stable stencils that make weights with desirable properties for differentiation matrix, we apply a greedy algorithm, then convergence and stability of proposed scheme are investigated theoretically and numerically to show efficiency of developed technique. Finally, numerical results are provided by some FPDEs in regular and irregular shaped domains to illustrate the approximation quality and convergence of our approach in comparison with the results presented in literatures. [ABSTRACT FROM AUTHOR]

This article proposes a numerical method to find the numerical solutions of the time-fractional diffusion equations involving fractional distributed order operator of Caputo type. Using the finite difference approach, we solve these equations by applying the semi-discrete method regarding the time variable and the fully-discrete method regarding the spatial variable. For the distributed integral part with respect to time, the Gauss–Legendre quadrature formula is applied and to estimate the multi-term time-fractional operator, including the Caputo fractional derivative, the L2 -1 approach is utilized. In addition, the error analysis and stability of the proposed numerical method are studied in this work. Finally, some numerical examples are provided to demonstrate the accuracy and efficiency of the suggested method. These examples are compared to several numerical previous methods stated in the articles, and the results show that the accuracy of our method is superior to these methods. [ABSTRACT FROM AUTHOR]

It is well known that spatial memory exists in animal movement modelling. Since spatial memory is related to the past information, then delay arises. In view of the protection of ecological environment, more and more scholars are concerned about the effects of toxic substances on it. A prey–predator system with memory-induced cross-diffusion and toxin in predator is considered in this paper. First, we discuss the fundamental dynamics in detail. Then considering the memory-induced cross-diffusion coefficient and the averaged memory period delay in predator as the controlling parameters, we get that n -mode Hopf bifurcations exist at the positive steady state. Stability switches are generated, and there are spatially nonhomogeneous periodic solutions. Namely if the cross-diffusion coefficient is small, the populations always coexist. If the cross-diffusion coefficient is moderate, two kinds of critical values of the averaged memory period of Hopf bifurcations occur and stability switches may be induced by the delay. If the cross-diffusion coefficient becomes larger, one kind of critical value of the averaged memory period of Hopf bifurcation occur. From simulations, the memory-based cross-diffusion and toxin have vital influences on stability. The moderate toxin can be good for population coexistence. When the averaged memory period is small, the toxin does not change the stability. Once the averaged memory period is bigger, the toxin can change the stability. Moreover, it shows that the averaged memory delay could switch the stability of the system. [ABSTRACT FROM AUTHOR]

This article discusses an efficient numerical method for solving nonlinear time-fractional integro-partial differential initial–boundary-value problems. To tackle the non-linearity of the problem, we first use the Newton linearization process. Then we apply the non-symmetric interior penalty Galerkin method for the spatial variable, and obtain a semi-discrete problem in the time variable. Finally, to obtain the fully-discrete scheme, we use both L1-scheme and L2-scheme for time-fractional derivative, and trapezoidal rule for integral term in the semi-discrete problem. We derive L 2 -norm stability and error estimates. The validity of the error analysis is supported by numerical experiments. [ABSTRACT FROM AUTHOR]

• Li 5 Mg@Cu | LFP exhibits a high-capacity retention of 91.8 % for 1000 cycles. • Li 5 Mg@Cu exhibits the excellent air and thermodynamic stability. • It offers a new perspective for finding the optimal component of Li-Mg alloys. • The stripping/plating behaviors of the Li x Mg alloy were investigated. • The effects of Mg doping on the suppression of dendrite growth were investigated. Li metal is widely recognized as the desired anode for next-generation energy storage, Li metal batteries, due to its highest theoretical capacity and lowest potential. Nonetheless, it suffers from unstable electrochemical behaviors like dendrite growth and side reactions in practical application. Herein, we report a highly stable anode with collector, Li 5 Mg@Cu, realized by the melting-rolling process. The Li 5 Mg@Cu anode delivers ultrahigh cycle stability for 2000 and 1000 h at the current densities of 1 and 2 mA cm–2, respectively in symmetric cells. Meanwhile, the Li 5 Mg@Cu|LFP cell exhibits a high-capacity retention of 91.8 % for 1000 cycles and 78.8 % for 2000 cycles at 1 C. Moreover, we investigate the suppression effects of Mg on the dendrite growth by studying the performance of Li x Mg@Cu electrodes with different Mg contents (2.0–16.7 at%). The exchange current density, surface energy, Li+ diffusion coefficient, and chemical stability of Li x Mg@Cu concretely reveal this improving suppression effect when Mg content becomes higher. In addition, a Mg-rich phase with "hollow brick" morphology forming in the high Mg content Li x Mg@Cu guides the uniform deposition of Li. This study reveals the suppression effects of Mg on Li dendrites growth and offers a perspective for finding the optimal component of Li-Mg alloys. [Display omitted] [ABSTRACT FROM AUTHOR]

Rumors have been widespread with the development of self-media, which has brought new challenges to government departments in dealing with rumor management. Considering the combined effect of the external refutation of media reports and the internal refutation of the counter individuals, the susceptible-infective-counter-media-remover (SICMR) rumor propagation model with a double refutation mechanism is proposed. The two thresholds for rumor propagation are obtained by mathematical analysis of the model. Based on the Jordan matrix theory and Routh-Hurwitz judgment, two rumor-free equilibriums (RFE) and four rumor-spread equilibriums (RSE) are obtained, and the stability of the equilibria is proved. The theoretical results and the influence of key parameters are verified by numerical simulation, and the validity of the model is verified through comparative experiments. Using the simulation data for function fitting, the results showed that the initial values of the media reports and the counter individuals are exponentially related to the peak of rumor propagation, respectively. Finally, based on two real rumor datasets of Twitter, the least square method is used to fit the model parameters. Through the comparison experiment with other similar works, the R-squared of the SICMR is 0.8811 and 0.9469 on two real datasets, respectively, which is the best result. [ABSTRACT FROM AUTHOR]

In this paper, based on the developed nonlinear fourth-order operator and method of order reduction, a novel fourth-order compact difference scheme is constructed for the mixed-type time-fractional Burgers' equation, from which L1-discretization formula is applied to deal with the terms of fractional derivative, and the nonlinear convection term is discretized by nonlinear compact difference operator. Then a fully discrete L1 compact difference scheme on uniform meshes can be established by approximating spatial second-order derivative with classic compact difference formula. The convergence and stability of the proposed scheme are rigorously proved in the L ∞ -norm by the energy argument and mathematical induction. We also establish a temporal second-order compact difference scheme on graded time meshes for solving the problem with weak initial singularity. Finally, several numerical experiments are provided to test the accuracy of two numerical schemes and verify the theoretical analysis. • The mixed-type time-fractional Burgers' equation which possesses the significant physical background has hardly been considered yet. • By the nonlinear fourth-order operator, a fully discrete compact difference scheme is established. • Based on the construction of (ii), the unconditional stability and convergence are deduced by the energy argument. • To illustrate the effectiveness of the implicit compact difference scheme, a fixed-point iterative algorithm is used to implement that. The numerical result is consistent with the theoretical analysis. [ABSTRACT FROM AUTHOR]

Forced convective heat transfer and boundary layer flow of non-Newtonian fluid over a moving wedge is numerically studied. The non-Newtonian fluid is represented by Carreau fluid which is inelastic and characterizes shear-thinning and shear-thickening fluid. The thermal conductivity of fluid is no longer constant during heat transfer but is a function of temperature. The motion of the wedge surface is considered in the direction of mainstream or opposite. Both wedge and mainstream flows are assumed as a power of distance from the origin. Upon using similarity transformations, resultant equations are analyzed numerically using Chebyshev collocation and shooting methods for simulations of solutions. Most of the general features of solutions are identical to Newtonian fluid, the effects of Carreau fluid are to increase the velocity and heat transfer rate, and decrease the thicknesses. The present results of Carreau fluid and heat transfer unveil single and double solutions for the same system parameters and are shown to be a continuation of the Newtonian fluid. Also, the non-uniqueness of the solutions for the same set of parameters is classified as first and second solutions. Thus, there is a critical point beyond which no solution exists to model. In order to identify which of these solutions can be simulated practically, we perform linear stability analysis on velocity and temperature solutions. The eigenvalue analysis shows that the first solutions are always stable and the second solutions are amplified in time. Other interesting flows and heat transfer features are discussed in detail. [Display omitted] • We study boundary layer flow and forced convective heat transfer in Carreau fluid. • We also include generalized thermal conductivity and viscous dissipation in model. • Governing equations are solved using Chebyshev collocation and shooting technique. • We experience the non-uniqueness of the model which produces the dual solutions. • Stability of dual solutions is analyzed using an eigenvalue approach. [ABSTRACT FROM AUTHOR]

Copyright of China Cleaning Industry / Zhongguo Xidi Yongpin Gongye is the property of China Cleaning Industry Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The yellow virus in the red chili fractional order model is investigated in this scientific study. The Caputo–Fabrizio and Fractal fractional derivative operator, which incorporates an antiretroviral treatment compartment, are used to investigates this pandemic occurrence. It is essential to figure out how to develop methods to halt the spread of the yellow virus in red chili. While measures are being taken to curb the pandemic of the yellow virus, the more contagious yellow virus found in red chilies is emerging in several areas. It is essential to develop methods for preventing the spread of the yellow virus. To maintain a certain level of protection while simulating the yellow virus's spread in red chili plants. We investigated the potential for an epidemic in red chili plants as a case study. In this study, we use fixed point theory to create existence, uniqueness, and stability conditions for the fractional order yellow virus in the red chilli model using the Caputo Fabrizio operator. For these kinds of biological models, the fractional derivative technique is quite new. By using the iterative Laplace transform approach, we have also discovered the initial approximate solutions for a suggested model that are readily available. This method combines the Laplace transform method with one of the most dependable methods, the new iterative method. Finally, we analysed parameters that represent the progression of sickness and used charts to display the numerical simulations. [ABSTRACT FROM AUTHOR]

In an attempt to illustrate the dynamics of the spread of scam rumors and its impact in a heterogeneous population or social network we adopt the epidemiological model approach. In this work the S p E I s S c S t (Susceptible, Exposed, Ignorant, Scammers and Stiflers) model was developed. A diagrammatic representation of the flow of individuals from one class/group to another is given from which a system of five differential equations are obtained. The Basic reproduction number, the equilibrium point of scam rumor-free and the endemic equilibrium state were obtained and discussed. For the local stability of the scam rumor-free and endemic equilibrium state the Next Generation Matrix was used. We were able to show the conditions for the existence of global stability by defining a Lyapunov function with respect to the state variables. Numerical simulation of the system was carried out in order to get a clear picture of the dynamics of the spread of scam rumor in a population or social networks, its impact in a population, and the efficiency of government/admin policies in curbing the spread of scam rumor. • The rumor model S p E I s S c S t was specific on the spread of scams. • The Next Generation Matrix was used for local stability of the model. • Lyapunov functions were define in order to show the existence of global stability. • The result shows that scam rumor-free equilibrium is locally if R 0 < 1. • Result also shows that scam rumor-free is globally asymptotically stable if R 0 < 1. [ABSTRACT FROM AUTHOR]

The "Middle East Respiratory" (MERS-Cov) is among the world's dangerous diseases that still exist. Presently it is a threat to Arab countries, but it is a horrible prediction that it may propagate like COVID-19. In this article, a stochastic version of the epidemic model, MERS-Cov, is presented. Initially, a mathematical form is given to the dynamics of the disease while incorporating some unpredictable factors. The study of the underlying model shows the existence of positive global solution. Formulating appropriate Lyapunov functionals, the paper will also explore parametric conditions which will lead to the extinction of the disease from a community. Moreover, to reveal that the infection will persist, ergodic stationary distribution will be carried out. It will also be shown that a threshold quantity exists, which will determine some essential parameters for exploring other dynamical aspects of the main model. With the addition of some examples, the underlying stochastic model of MERS-Cov will be studied graphically for more illustration. [ABSTRACT FROM AUTHOR]

Acmella oleracea is an ethnobotanically significant plant with a relatiwely high content of spilanthol. Due to its broad spectrum of activity, including anti-inflammatory, antioxidant, analgesic, antifungal, and bacteriostatic properties, it is considered a valuable bioactive natural product. In addition, spilanthol as its main bioactive component inhibits facial muscle contractions, making it an attractive ingredient in anti-wrinkle and anti-aging cosmetics. Due to its muscle paralyzing effects, it is called herbal botox. The commercial interest in spilanthol encourages the development of effective methods of isolating it from plant material. The methodology used in this paper allows for the obtaining of extracts from Acmella oleracea with a relatively high content of spilanthol. An effective method of spilanthol extraction from all aerial parts of Acmella oleracea as well as methods of enriching spilanthol concentration in extracts achieved by removing polar and acidic substances from crude extracts was developed. To quantify the concentration of spilanthol, a simple, fast and economically feasible quantification protocol that uses nuclear magnetic resonance (HNMR) was developed. In addition, it has been proven, that oxidation of spilanthol by air gives (2 E ,7 Z)-6,9-endoperoxy- N -(2-methylpropyl)-2,7-decadienamide. The studies on spilanthol solutions stability were carried out and the conditions for the long-time storage of spilanthol solutions have also been developed. Additionally, for confirmation of obtained results a sensitive (LOQ=1 ng/mL), precise (RSD lower than 7%) and accurate (RE lower than 7.5%), new HPLC-MS/MS method was applied. [ABSTRACT FROM AUTHOR]

Rumors do the social's perception seal, leaving people untouched with the true thing. Since the harmfulness of rumors is well known, in order to cut off the net of rumors and make the society run in order, it is necessary to have a deeper understanding of the spread of rumors. In this paper, the non-smooth reaction–diffusion system with considering the encouraging effect of secondary propagation of Internet platform on rumor propagation is used to study the dynamic system of rumor propagation. Firstly, the existence of the non-negative solution is proved by using the theory of upper and lower solutions for mixed monotone system. Secondly, the value of the basic reproduction number is calculated and the existence of positive equilibrium are discussed. Thirdly, the backward bifurcation and the saddle-node bifurcation are investigated. Fourthly, the stability of rumor propagation equilibrium and Hopf bifurcation are analyzed theoretically. Finally, some numerical simulations which proves the validity of the above theory are provided. [ABSTRACT FROM AUTHOR]

• Fully solution-derived GQDs-IGZO TFTs based on ZrO x as gate dielectrics have been achieved. • GQDs-IGZO TFTs devices with optimized doping content have demonstrated improved performances, including a μ FE of 35.91 cm2 V–1 s–1, a higher I ON / I OFF of 5.04 × 108, a smaller subthreshold swing (SS) of 0.11 V dec–1 and a smaller interfacial trap states of 1.57 × 1012 cm−2. • Resistor-loaded unipolar inverter based on GQDs-IGZO/ZrO x has been integrated, demonstrating good dynamic behavior and a high gain of 9.3. • LFN characteristics of GQDs-IGZO/ZrO x TFTs have suggested that the fluctuations in mobility are the noise source. This work presents solution-processed high-performance graphene quantum dots (GQDs) decorated amorphous InGaZnO (α-IGZO) thin-film transistors (TFTs) based on ZrO x as gate dielectrics. Compare with pure IGZO TFTs, GQDs-modified α-IGZO TFTs devices with optimized doping content have demonstrated better performances, including a larger field-effect mobility (μ FE) of 35.91 cm2 V–1 s–1, a higher on/off current ratio (I ON / I OFF) of 5.04 × 108, a smaller subthreshold swing (SS) of 0.11 V dec–1 and a smaller interfacial trap states (D it , 1.57 × 1012 cm−2). Moreover, the GQDs-doped IGZO TFTs with a doping concentration of 0.5 mg ml–1 have shown excellent stability under bias stress and illumination stress conditions. To demonstrate the potential applications of α-IGZO TFTs in logic circuits, a resistor-loaded unipolar inverter based on GQDs-IGZO/ZrO x has been integrated, demonstrating good dynamic behavior and a high gain of 9.3. Low-frequency noise (LFN) characteristics of GQDs-IGZO/ZrO x TFTs have suggested that the fluctuations in mobility are the noise source. Based on all the experimental findings, it can be concluded that solution-processed GQDs-IGZO/ZrO x TFT may envision promising applications in optoelectronics. [Display omitted] [ABSTRACT FROM AUTHOR]

A finite difference method for time-fractional Klein–Gordon equation with the fractional order α ∈ (1 , 2 ] on an unbounded domain is studied. The artificial boundary conditions involving the generalized Caputo derivative are derived using the Laplace transform technique. Stability and error estimates of the proposed finite difference scheme are proved in detail by using the discrete energy method. Numerical examples show that the artificial boundary method is a robust and efficient method for solving the time-fractional Klein–Gordon equation on an unbounded domain. [ABSTRACT FROM AUTHOR]

In this study, a stability and stabilization analysis is discussed for Takagi–Sugeno (T-S) fuzzy systems with distributed time-delays. A fuzzy-based memory state-feedback control is designed to stabilize the delayed T-S fuzzy systems. A new Lyapunov–Krasovskii functional is constructed in an augmented form with information about the lower and upper bounds. Based on this functional, asymptotic stability of the closed-loop T-S fuzzy systems is achieved, and sufficient conditions are derived in linear matrix inequality form. In the numerical example section, comparative results are given with their simulation results to show the merits of the proposed approach and control scheme. • This study focuses on the stability problem of distributed delayed T-S fuzzy systems. • An augmented type of Lyapunov–Krasovskii functional is built with delay information. • A state-feedback controller is constructed to stabilize the delayed T-S fuzzy system. • Conservative results are obtained by employing GFWMA inequality. • Numerical examples provide the strength of this work compared with the existing work. [ABSTRACT FROM AUTHOR]

Hydatid disease is a chronic zoonotic parasitic disease caused by Echinococcus. This paper proposes and analyzes a mathematical model of Echinococcosis disease system with a piecewise control function concerning threshold policy. The model is represented the control measures being triggered once the total number of infected hosts and human reaches the tolerant level. Model solutions are able to approach either one real equilibrium or the pseudo-equilibrium, depending on the tolerant threshold. Our results suggest that in order to diminish the outbreak of Echinococcosis or lead the number of infecteds to an expected level, it requires not only adequate hospital resources and certain government interventions, but also a good threshold policy. [ABSTRACT FROM AUTHOR]

A compact difference operator is a valuable technique which has been used to develop numerical schemes capable of solving various types of differential equations. Advantages of compact procedures include obtaining high accuracy with a relatively small number of grid points. In this paper, we introduce weighted parameters in standard compact difference operators. Therefore, applications of both high-order compact finite difference operators for spatial derivatives and the Crank–Nicolson/Adams–Bashforth method for temporal derivatives have been used to solve coupled BBM equations. As the consequence system of equations is uncoupled during computing, it requires less CPU processing time. In addition, when producing numerical solutions, the system equations obtained at each time step are constant-coefficient matrices, gaining a remarkable number of computational advantages. In addition, deriving an a priori estimate of numerical solutions obtains convergence and stability analyses. Simultaneously, the algorithm is globally structure-preserving as to the negligence of nonphysical behavior. Numerical results demonstrate that the proposed weighted compact finite difference scheme can improve the computational efficiency of standard second-order methods. Additionally, appropriately weighted parameters can refine numerical accuracy. Lastly, an investigation of the relevant properties of numerically computed solutions is conducted, including a finite time blow-up of a head-on collision and a two-way wave propagation. [ABSTRACT FROM AUTHOR]

Copyright of China Pulp & Paper Industry is the property of China Pulp & Paper Industry Publishing House and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations is to render their hyperbolic character to elliptic form. This paper is devoted to the study of a stabilized linear, domain decomposition, finite element method for the time harmonic Maxwell's equations, in a dual form, obtained through the Laplace transformation in time. The model problem is for the particular case of the dielectric permittivity function which is assumed to be constant in a boundary neighborhood. The discrete problem is coercive in a symmetrized norm, equivalent to the discrete norm of the model problem. This yields discrete stability, which together with continuity guarantees the well-posedness of the discrete problem, cf Arnold et al. (2002) [3] , Di Pietro and Ern (2012) [45]. The convergence is addressed both in a priori and a posteriori settings. In the a priori error estimates we confirm the theoretical convergence of the scheme in a L 2 -based, gradient dependent, triple norm. The order of convergence is O (h) in weighted Sobolev space H w 2 (Ω) , and hence optimal. Here, the weight w ≔ w (ɛ , s) where ɛ is the dielectric permittivity function and s is the Laplace transformation variable. We also derive, similar, optimal a posteriori error estimates controlled by a certain, weighted, norm of the residuals of the computed solution over the domain and at the boundary (involving the relevant jump terns) and hence independent of the unknown exact solution. The a posteriori approach is used, e.g. in constructing adaptive algorithms for the computational purposes, which is the subject of a forthcoming paper. Finally, through implementing several numerical examples, we validate the robustness of the proposed scheme. [ABSTRACT FROM AUTHOR]