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The current study explores the transient magnetohydrodynamic (MHD) flow with the interaction of quadratic convection, slip of second‐order momentum, viscous dissipation, and Newtonian heating. In this setup, the governing equations become highly nonlinear. The numerical solutions are attained by utilizing an implicit type of the Crank–Nicolson technique. The primary aim of the exploration is to figure out the consequence of MHD nonlinear convection and momentum slip of second‐order on the overall behavior of the system. The robust agreement is evinced by numerical computations verified against existing research. Skin friction and Nusselt number decreases for second‐order slips, δ=0,−2,−4,−8 $\delta =0,-2,-4,-8$, and −16. And for γ=1.0 $\gamma =1.0$ and δ=‐2.0 $\delta = \mbox{-} 2.0$ the temporal coefficients of friction and heat transmission attain a steady state at time t = 29.88. It is significant that nonlinear convection predominates over viscous dissipation and that nonlinear convection is influenced by magnetic fields. The results are described using plots and tables. [ABSTRACT FROM AUTHOR]

During the oilfield development process, various factors can cause different types of reservoir damage, leading to reduced oil well production or even shutdown, and decreased water injection capacity in water wells, resulting in significant economic losses for the oilfield. However, formation damage control measures must be based on the quantitative diagnosis of the types and degrees of reservoir damage. This paper establishes a spatiotemporal evolution numerical model for 12 common types of damage during the oil and gas exploration and development process, based on the material balance theory and Fick's diffusion law in reservoir damage processes. This model achieves numerical simulation of the degree of various reservoir damage types in different spatiotemporal domains. The overall damage degree of a specific well's evolution with time and space is further simulated in simple superposition way. The sequential core flow experiment was carried out in the laboratory, and then compared with the calculation results. The accuracy is above 90%. Finally, using field test data, the simulation results show a 95% or higher degree of agreement with the actual field measurements, proving that the reservoir damage spatiotemporal evolution quantitative simulation technology established in this paper has high accuracy and practicality. [ABSTRACT FROM AUTHOR]

This paper aims to investigate some new dynamics of a new model describing the rabies virus dynamics, taking into account the effect of proper vaccination. The model's population is divided into three main compartments, namely, susceptible S(t), infected I(t), and recovered R(t) individuals. The model is formulated and then the equilibrium points of the model are found. The local and global stabilities of equilibrium points of the proposed model are investigated where conditions of stability are attained in terms of key parameters in the model. Bifurcation analysis is performed for the possible occurrence of codimension‐one bifurcations in the model. In addition, bifurcation surfaces are plotted in the space of parameters in the model. For the numerical verification, a nonstandard finite difference method is adapted for solving the model and the accurate results of numerical simulations are depicted to reveal the dynamics of the model. The method provides realistic data for the model and these data can be used to predict the spread of the virus and to provide insight into proper procedures and control measures that can be taken. [ABSTRACT FROM AUTHOR]

Grid-Nesting is a common method of local refinement when using structured quadrilateral grid in estuarine models. Nevertheless, various issues need to be improved, such as the Courant-Friedrichs-Lewy (CFL) limitations of external gravity wave and information exchange between two-way nesting grids. Based on the material conservation law, a novel scheme with Implicit, Grid-Nesting Elevation Solution (IGNES) and matched Nesting Boundary Flux Conservation Interpolation (NBFCI) was developed in this paper. The unstructured quadrilateral grid, finite-differencing, estuarine and coastal ocean model (UFDECOM) was update to UFDECOM-i. The gravity wave propagation experiment shows that the IGNES can relax the CFL limitations. Compared to traditional i-j two-direction strip refinement, the new scheme has higher computational efficiency. When the root-mean-square-error of elevation and current velocity increases by less than 0.05% and 0.2%, the calculation time is reduced by 40%. When simulating vortex motion, it overcomes the problem of simulation collapse caused by errors in nested boundaries. When simulating material transport, NBFCI scheme has smaller errors at the nesting boundary compared to quadratic interpolation, the high-order spatial interpolation at the middle temporal level (HSMIT) parabolic interpolation, upwind Advection-Equivalent interpolation, and HSIMT Advection-Equivalent interpolation scheme. The simulation results of the severe saltwater intrusion in the Changjiang Estuary in the late summer and early autumn of 2022 demonstrate that the UFDECOM-i with NBFCI and IGNES has higher computational efficiency and accuracy. [ABSTRACT FROM AUTHOR]

The discrete-time and discrete-space model for stochastic nonlocal shunting inhibitory cellular neural networks with reaction diffusions are modelled in the first time. Owing to the consideration of spatial variables, the discrete model derived in this article is more complex than the traditional ordinary difference model. In accordance with the constant-variation-formula for discrete-time and discrete-space model, Banach contracting mapping principle, the method of proof by contradiction and stochastic calculus, we also obtain the existence of a unique bounded almost periodic sequence for the discrete model, which is exponentially stable in the mean-square sense. Noting that it is the first time to consider the dynamics of almost periodicity in distribution of time-space discrete neural network models. The practicability of the present results is demonstrated by means of an illustration. [ABSTRACT FROM AUTHOR]

The uniform exponential stabilities (UESs) of two hybrid control systems comprised of a wave equation and a second‐order ordinary differential equation are investigated in this study. Linear feedback law and local viscosity are considered, as are nonlinear feedback law and internal anti‐damping. The hybrid system is first reduced to a first‐order port‐Hamiltonian system with dynamical boundary conditions, and the resulting system is discretized using the average central‐difference scheme. Second, the UES of the discrete system is obtained without prior knowledge of the exponential stability of the continuous system. The frequency domain characterization of UES for a family of contractive semigroups and the discrete multiplier approach are used to validate the main conclusions. Finally, the Trotter–Kato theorem is used to perform a convergence study on the numerical approximation approach. Most notably, the exponential stability of the continuous system is derived by the convergence of energy and UES, which is a novel approach to studying the exponential stability of some complex systems. Numerical simulation is used to validate the effectiveness of the numerical approximating strategy. [ABSTRACT FROM AUTHOR]

This paper extends the valuation and optimal surrender framework for variable annuities with guaranteed minimum benefits in a Lévy equity market environment by incorporating a stochastic interest rate described by the Hull-White model. This approach frames a more dynamic and realistic financial setting compared to previous literature. We exploit a robust valuation mechanism employing a hybrid numerical method that merges tree methods for interest rate modeling with finite difference techniques for the underlying asset price. This method is particularly effective for addressing the complexities of variable annuities, where periodic fees and mortality risks are significant factors. Our findings reveal the influence of stochastic interest rates on the strategic decision-making process concerning the surrender of these financial instruments. Through comprehensive numerical experiments, and by comparing our results with those obtained through the Longstaff-Schwartz Monte Carlo method, we illustrate how our refined model can guide insurers in designing contracts that equitably balance the interests of both parties. This is particularly relevant in discouraging premature surrenders while adapting to the realistic fluctuations of financial markets. Lastly, a comparative statics analysis with varying interest rate parameters underscores the impact of interest rates on the cost of the optimal surrender strategy, emphasizing the importance of accurately modeling stochastic interest rates. [ABSTRACT FROM AUTHOR]

Computationally extensive fluid flow simulations usually require numerical schemes with a high degree of numerical precision, where high wavenumber and frequency capturing capability is desired in solutions with high physical fidelity. Numerical dispersion and diffusion errors must be reduced to a minimum in order to caputre low amplitude and high frequency flow aspects, such as flow induced sound waves and minor instabilities. Such schemes also must be capable of dealing with flow discontinuities, such as shockwaves and expansion waves in cases where the flow velocity stands near or above sound velocity. In this work the Dispersion Relation Preserving (DRP) optimization is formally extended to the compact Finite Volume (FV) framework where the error is minimized along a given spectral interval. This is done by equaling the resulting algebraic compact spectral optimized Finite Difference (FD) operators with the Finite Volume formulation with the desired numeric characteristics. Numerical tests are carried over linear and nonlinear governing equations models for one and three-dimensional cases, where the travelling Gaussian wave, the transient expansion wave and the smooth to nonsmooth step wave flows are considered. The proposed compact DRP FV schemes surpasses its counterparts in some numerical tests while maintaining comparable capabilities with other more basic schemes in the remaining numerical tests. Excellent broadband content capturing capability is observed, while possessing reduced numerical instabilities generation. [ABSTRACT FROM AUTHOR]

In this paper, mathematical model of heat transfer in a porous fin with internal heat generation, and thermal conductivity is influenced by both spatial factors and temperature are examined. These two concepts are integrated into the model, which highlighting the originality of the current study. The equations and conditions that govern the system are expressed in a dimensionless manner. We examine three scenarios for thermal conductivity: constant, linear, and exponential dependence on temperature. We have utilized three different techniques to solve the problem, including the Legendre Wavelet Collocation, Finite Difference, and Least Square. Due to the nonlinearity of the presented problem, it is not possible to find an exact analytical solution. In this specific scenario, we calculate exact solution, which is then compared to these three methods and found to have a good agreement. The findings and error assessment are displayed in figures and tables. The Legendre wavelet collocation approach yields high accuracy. The novelty of the research is the implantation of space and temperature dependent thermal conductivity and solution of a complex nonlinear problem using a hybrid numerical technique, specifically the collocation method with Legendre Wavelet basis functions. [ABSTRACT FROM AUTHOR]

Producing spatial transformations that are diffeomorphic is a key goal in deformable image registration. As a diffeomorphic transformation should have positive Jacobian determinant | J | everywhere, the number of pixels (2D) or voxels (3D) with | J | < 0 has been used to test for diffeomorphism and also to measure the irregularity of the transformation. For digital transformations, | J | is commonly approximated using a central difference, but this strategy can yield positive | J | 's for transformations that are clearly not diffeomorphic—even at the pixel or voxel resolution level. To show this, we first investigate the geometric meaning of different finite difference approximations of | J | . We show that to determine if a deformation is diffeomorphic for digital images, the use of any individual finite difference approximation of | J | is insufficient. We further demonstrate that for a 2D transformation, four unique finite difference approximations of | J | 's must be positive to ensure that the entire domain is invertible and free of folding at the pixel level. For a 3D transformation, ten unique finite differences approximations of | J | 's are required to be positive. Our proposed digital diffeomorphism criteria solves several errors inherent in the central difference approximation of | J | and accurately detects non-diffeomorphic digital transformations. The source code of this work is available at https://github.com/yihao6/digital_diffeomorphism. [ABSTRACT FROM AUTHOR]

The performance of the porous gas bearing depends on the geometric characteristics, material, fluid properties, and the properties of the porous media, which is a restrictor that controls the gas flow. Its application in industrial environments must support higher loads, higher supply pressure, and, consequently, higher pressure in the lubricant fluid film. Because porous media has a relatively low elastic modulus, it is necessary to consider its deformation when designing porous gas bearings. The design of porous gas bearings is a multi-objective problem in engineering because the optimization objectives commonly are to maximize the load capacity or static stiffness coefficient and minimize the airflow; these objectives conflict. This work presents a multi-objective optimization algorithm based on the nature-inspired Flower Pollination Algorithm enhanced with Non-Dominated Sorting Genetic Algorithm II. The algorithm is applied to optimize the design of a porous gas bearing, maximizing the resultant force and the static stiffness coefficient and minimizing the airflow. The results indicate a better performance of the Multi-Objective Flower Pollination Algorithm than the Multi-Objective Cuckoo Search. The results show a relatively short running time of 6 min for iterations and a low number of iterations of 50. [ABSTRACT FROM AUTHOR]

After tunnel excavation and unloading, the stress state of the rock mass is redistributed, resulting in varying radial stresses at different radial depths in the rock mass. Rock mechanics tests showed that the confining pressure, especially for soft rock, had a substantial impact on the mechanical properties of the rock which at various radial depths varied with the confining pressure. Therefore, the Mohr-coulomb strength criterion was used in this study to elastic-plastic analysis of deeply buried tunnels that took into account the coupling impact of strain-softening and confining pressure using the finite difference method. Then, regardless of whether the confining pressure is taken into account, the rock mass's plastic zone radius and deformation value were compared, which were considerably impacted by confining pressure: the effect is more pronounced when the rock strength is lower and the initial geostress is higher. The rock mass's strain-softening behaviors and its confining pressure effect should be highlighted while soft rock tunnel support structures were designed with the condition of high initial geostress in order to prevent the rock mass's distinct deformation of the rock mass caused by the calculation results distortion or even serious consequences like large deformation, damage or failure. [ABSTRACT FROM AUTHOR]

Copyright of Railway Standard Design is the property of Railway Standard Design 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.)

We construct a quasi-conservative alternative WENO finite difference scheme respectively coupled with the global Lax-Friedrichs (AWENO-GLF) and the contact restored Harten-Lax-van Leer approximate Riemann solver (AWENO-HLLC) for solving compressible multicomponent flows. The mass equation, the momentum equation, and the energy equation are discretized by a fully conservative AWENO-GLF or AWENO-HLLC finite difference scheme from which a consistent nonconservative discretization of the topological equation is derived according to the velocity and pressure equilibrium principle proposed by Agrall (J Comput Phys 125:150–160, 1996). We prove that, coupling with the constructed scheme, WENO interpolations with common weights for conservative variables or standard WENO interpolations with independent weights for primitive quantities can maintain velocity and pressure equilibrium. Numerical examples demonstrate that AWENO-HLLC scheme is not only less dissipative but also less oscillatory than classical WENO-GLF scheme for compressible multicomponent flows. [ABSTRACT FROM AUTHOR]

Nonstandard finite-difference (NSFD) methods, pioneered by R. E. Mickens, offer accurate and efficient solutions to various differential equation models in science and engineering. NSFD methods avoid numerical instabilities for large time steps, while numerically preserving important properties of exact solutions. However, most NSFD methods are only first-order accurate. This paper introduces two new classes of explicit second-order modified NSFD methods for solving n-dimensional autonomous dynamical systems. These explicit methods extend previous work by incorporating novel denominator functions to ensure both elementary stability and second-order accuracy. This paper also provides a detailed mathematical analysis and validates the methods through numerical simulations on various biological systems. [ABSTRACT FROM AUTHOR]

Abstract During the oilfield development process, various factors can cause different types of reservoir damage, leading to reduced oil well production or even shutdown, and decreased water injection capacity in water wells, resulting in significant economic losses for the oilfield. However, formation damage control measures must be based on the quantitative diagnosis of the types and degrees of reservoir damage. This paper establishes a spatiotemporal evolution numerical model for 12 common types of damage during the oil and gas exploration and development process, based on the material balance theory and Fick’s diffusion law in reservoir damage processes. This model achieves numerical simulation of the degree of various reservoir damage types in different spatiotemporal domains. The overall damage degree of a specific well’s evolution with time and space is further simulated in simple superposition way. The sequential core flow experiment was carried out in the laboratory, and then compared with the calculation results. The accuracy is above 90%. Finally, using field test data, the simulation results show a 95% or higher degree of agreement with the actual field measurements, proving that the reservoir damage spatiotemporal evolution quantitative simulation technology established in this paper has high accuracy and practicality.

The performance of the porous gas bearing depends on the geometric characteristics, material, fluid properties, and the properties of the porous media, which is a restrictor that controls the gas flow. Its application in industrial environments must support higher loads, higher supply pressure, and, consequently, higher pressure in the lubricant fluid film. Because porous media has a relatively low elastic modulus, it is necessary to consider its deformation when designing porous gas bearings. The design of porous gas bearings is a multi-objective problem in engineering because the optimization objectives commonly are to maximize the load capacity or static stiffness coefficient and minimize the airflow; these objectives conflict. This work presents a multi-objective optimization algorithm based on the nature-inspired Flower Pollination Algorithm enhanced with Non-Dominated Sorting Genetic Algorithm II. The algorithm is applied to optimize the design of a porous gas bearing, maximizing the resultant force and the static stiffness coefficient and minimizing the airflow. The results indicate a better performance of the Multi-Objective Flower Pollination Algorithm than the Multi-Objective Cuckoo Search. The results show a relatively short running time of 6 min for iterations and a low number of iterations of 50.

The asymmetric wave equation encompasses the influence of the actual fine structure inside the medium on the wave field, which can better represent the complex seismic wavefield excited by the complex source and reflect the scale effects of the seismic wave response under equal computational power. However, when the finite-difference (FD) operator is applied to implement the numerical modelling using the asymmetric wave equation, numerical dispersion appears due to the use of difference operator to approximate the differential operator, which negatively affects the analysis of the seismic wavefield. To suppress the numerical dispersion, this paper proposes an improved Dung Beetle optimization (IDBO) algorithm to obtain the optimized FD operators. The IDBO algorithm adopts an improved Tent map and the opposition-based learning strategy to initialize the population, which improves the diversity of the population. The nonlinear function adaptive control strategy is introduced to adjust the population allocation ratio and boundary selection parameter R to achieve an adequate balance between global exploration and local exploitation. In addition, adaptive weights and the Levy flight mechanism are combined to improve the ball-rolling dung beetle position updating strategy to avoid falling into local extremes. Numerical dispersion analysis and numerical modelling results demonstrate that the optimization of FD operators based on the IDBO algorithm can effectively suppress numerical dispersion. It is of great significance to extract the wave field perturbation caused by heterogeneity due to the complex microstructure in the medium and analyse the influence of the microstructural properties in the medium on seismic wave propagation. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to propose a high order numerical method based on the finite difference methods for solving nonlinear Itˆo stochastic Volterra integral equations (SVIEs) of the second kind. To develop the method, a fourth-order implicit finite difference method and the explicit Milstein method are implemented for the discretization of non-stochastic and stochastic integral parts, respectively. To solve the original SVIEs, the proposed method has the deterministic fourth-order and strong stochastic first-order accuracy. The convergence analysis of the proposed method is proved. The finite difference method under consideration requires solving a 2×2 system of equations at each step for one-dimensional SVIE. Therefore, the proposed method is very simple to implement and does not require a lot of computational cost. Some numerical examples are prepared to indicate the verity and efficiency of the new method. Moreover, the comparative numerical results show that this method is more accurate than those existing methods given in the literature.

Heat transfer can be defined as transfer of energy from one area to another as a result of temperature differences in objects. This indicates heat transfer not only explains how heat energy is transferred from one object to another, but can also predict the rate of heat transfer that occurs under certain conditions. In this case, what is related to the heat flow model equation is two-chamber thermos separator where the separator is made of polypropylene. This separator functions to prevent the flow of heat from one side to the other side of the thermos tube. Polypropylene is included in the insulator category, although heat transfer still occurs. The heat transfer will be calculated using the finite difference method in parabolic partial differential equations using the Matlab application. The heat transfer process is assumed to occur by conduction, with a separator length of 1 cm. Assume the first side of the divider has a right temperature of 100°c, and the other side 20°c. The temperature point measured on the separator is located in the center of the separator. After completing the solution using the Matlab application with the finite difference method, a heat transfer flow simulation was obtained in the two-chamber thermos separator which shows the heat flow transfer at any time. At 0.1 seconds the temperature at T1 is 2.4°c, while at 10 seconds is 65.9704°c. Then at 0.1 seconds the temperature at T4 is 0.48°c, while at 10 seconds 19.5436°c. The conclusion is in the separator of the two-chamber thermos there is significant heat flow from the side of the first tube to the other side.

Induced polarization (IP) tomography measurements as a near-surface geophysical method can provide information about the degree of chargeability of subsurface materials, and are commonly used in mineral exploration, engineering studies (e.g., sediment/bedrock interface identification, crushed zones and faults detection, and landslide and soil properties imaging.), as well as in environmental investigations (contaminant plums identification and landfill characterization). The purpose of these measurements is to obtain the distribution of polarizability characteristics inside an object, generally below the surface, at the boundary of the object, or outside the area in question. The result of such measurements can be mathematically modeled for the specific polarizability properties by the solution of Poisson’s equation restricted by appropriate boundary conditions. In this paper, we focus on the importance of simulating induced-polarization responses and retrieving chargeability distributions in geo-materials to enhance the characterization of subsurface structures. We present the methods for forward modeling and nonlinear inversion of induced-polarization measurements. To this end, in the first step, Poisson’s equation for a two-dimensional ground with arbitrary distribution of conductivity is solved using the finite difference numerical method and in the next step, based on the existing relations between conductivity and chargeability (Siegel’s formulation), the apparent induced polarization response is calculated. Finally, we solve the nonlinear chargeability inversion problem following a nonlinear apparent resistivity inversion. This is achieved by imposing physical constraints to prevent the estimation of unrealistic model parameters, using a Newton-based optimization method. To evaluate the efficiency of the proposed methodology, we utilized the proposed algorithm to two simulated examples and a real data set. Our numerical results show that the algorithm reliably represents the main features and structure of the Earth’s subsurface in terms of the resistivity and chargeability models. All the algorithms presented in this paper have written in the MATLAB programming language.

The isotropy is a fundamental requirement for solving partial differential equations by the finite difference scheme. In this work, we first introduce the concept of the virtual nodes to construct the finite difference scheme, and propose several stencils of finite difference discretization to optimize the isotropy of the gradient and Laplacian operators. The isotropic error of the optimized gradient stencil is reduced to 4.1% and 7.5% of the conventional scheme and the typical 4th-order isotropic stencil that is widely used in the multiphase lattice Boltzmann method, while the optimized Laplacian stencil displays the best performance in the Fourier analysis. Then, the optimized stencils are applied to suppress the spurious currents in the multiphase lattice Boltzmann method. The spurious current is reduced to only 7.2% of that calculated by the typical 4th-order isotropic stencil at the reduced temperature 0.6, at which the liquid/gas density ratio is near to 1000. Furthermore, they are adopted to rectify the dendrite directions in the alloy solidification simulations by the phase field method. The angle deviation of dendrite growth is reduced to 15.7% of the conventional scheme. [ABSTRACT FROM AUTHOR]

Machine learning (ML) is becoming a powerful tool in Computational Fluid Dynamics (CFD) to enhance the accuracy, efficiency, and automation of simulations. Currently, in the design of shock-capturing methods, there is still a heavy reliance on the expertise and scientific knowledge of each author, particularly in nonlinear components such as smoothness indicators and weighting functions. ML has the potential to reduce this dependency, since by leveraging large datasets, they can learn intricate patterns and make accurate predictions of these functions. In this work we present a neural network that compute the weighting functions in the WENO5 scheme. The proposed WENO5-NN scheme generalizes well for different resolutions, and in most of the cases tested, it outperforms the classical WENO5-JS scheme. • Neural network to compute the weighting functions for WENO5 schemes. • The proposed scheme generalizes for different grid resolutions and problems. • The neural-network based scheme outperforms several WENO5 schemes. [ABSTRACT FROM AUTHOR]

In this study, the energy control and asymptotic stability of the 1D sine-Gordon equation were investigated from the viewpoint of numerical approximation. An order reduction method was employed to transform the closed-loop system into an equivalent system, and an average-central finite difference scheme was constructed. This scheme is not only energy-preserving but also possesses uniform stability. The discrete multiplier method was utilized to obtain the uniformly asymptotic stability of the discrete systems. Moreover, to cope with the nonlinear term of the model, a discrete Wirtinger inequality suitable for our approximating scheme was established. Finally, several numerical experiments based on the eigenvalue distribution of the linearized approximation systems were conducted to demonstrate the effectiveness of the numerical approximating algorithm. [ABSTRACT FROM AUTHOR]

This study introduces a novel numerical method for analyzing the nonlinear behavior of intricate electromagnetic structures, with a specific focus on a metatronic amplifier as a case study. We propose a modified approach that integrates Harmonic Balance (HB) and Finite Difference Frequency Domain (FDFD) methods, tailored for structures featuring anisotropic materials. The combined application of HB-FDFD enables a comprehensive investigation of spatial electromagnetic field distributions and harmonic responses within such structures. Moreover, this method effectively addresses the challenges associated with complex architectures. Additionally, we emphasize the incorporation of effective boundary conditions, as discussed in the paper, to enhance the accuracy of our analysis. Through a comparison with conventional methods, we demonstrate the efficacy of our approach and underscore its broad applicability to various nonlinear electromagnetic devices. [ABSTRACT FROM AUTHOR]

We present algorithms for constructing and resolving spectral problems for novel photonic crystal surface-emitting lasers with large emission areas, given by first-order PDEs with two spatial dimensions. These algorithms include methods to overcome computer-arithmetic-related challenges when dealing with huge and small numbers. We show that the finite difference schemes constructed using relatively coarse numerical meshes enable accurate estimation of several major optical modes, which are essential in practical applications. [ABSTRACT FROM AUTHOR]

In this work, we introduce two accurate and efficient finite difference methods based on radial basis functions (RBF–FD) for pricing European and American options under liquidity shocks. The problem is formulated as the semi-linear complementarity and PDE systems for American and European options, respectively. In the context of temporal semi-discretization, we provide two backward difference formulas of order one and two (BDF1 & BDF2). Furthermore, we discuss the stability and convergence properties of the proposed methods. For the American option, to solve the semi-linear system of complementarity problems (LCPs), we combine the RBF-FD approaches with an operator splitting (OS) method. To illustrate the efficiency and accuracy of the suggested methods, we provide numerical examples for both European and American call options and verify them with the existing work in the literature. In numerical discussion, we show the Greeks (Delta & Gamma) plots for the American options. [ABSTRACT FROM AUTHOR]

In this paper, we find some conditions under which a sequence \{\alpha (n)\} will satisfy the Laguerre inequality of any order asymptotically. Using this method, we prove that for any r and some constant c, the Maclaurin coefficients \gamma (n) of the Riemann Xi-function satisfy the Laguerre inequality of order r when n>cr^3, which provides a necessary condition for the Riemann hypothesis. We also prove that the partition function satisfies the Laguerre inequality of order r\geq 5 when n\geq 6r^4. As a consequence, it gives an affirmative answer to Wagner's conjecture on the threshold for the Laguerre inequalities of order no more than 10 for the partition function. Moreover, motivated by the study of Craven and Csordas on the complete monotonicity of the Maclaurin coefficients of entire functions in Laguerre-Pólya class, we consider the complete monotonicity of the sequences \{\alpha (n)\}. We give the criteria for the asymptotically complete monotonicity of the sequence \{\alpha (n)\} and \{\log \alpha (n)\}, respectively. With this criteria, we show that (-1)^r \Delta ^r \gamma (n)>0 for n>ce^{r^3} and (-1)^{r-1} \Delta ^r \log \gamma (n)>0 for n>cr^2. Furthermore, we propose some open problems. [ABSTRACT FROM AUTHOR]

We propose a new alternating direction method of multipliers (ADMM) with an optimal parameter for the unilateral obstacle problem. We first use the five-point difference scheme to discretize the problem. Then, we present an augmented Lagrangian by introducing an auxiliary unknown, and an ADMM is applied to the corresponding saddle-point problem. Through eliminating the primal and auxiliary unknowns, a pure dual algorithm is then used. The convergence of the proposed method is analyzed, and a simple strategy is presented for selecting the optimal parameter, with the largest and smallest eigenvalues of the iterative matrix. Several numerical experiments confirm the theoretical findings of this study. [ABSTRACT FROM AUTHOR]

AbstractThe Newton-Krylov method with the explicit Jacobian matrix is an efficient numerical method for solving the nuclear reactor nonlinear multiphysics coupling system. Compared with the Jacobian-free Newton-Krylov (JFNK) method, it has a better preconditioner matrix (the Jacobian matrix itself) and can achieve a more stable and faster convergence. How to compute the Jacobian matrix efficiently is a key issue for this method. The graph coloring algorithm is an essential technique and has been used to reduce the Jacobian computational burden by exploiting its sparsity. The fewer the coloring numbers in the Jacobian, the less the Jacobian computational cost will be. Besides, when computing the Jacobian in a distributed memory parallel environment, the parallel graph coloring algorithms are required because the Jacobian is distributed among processors. Currently, a popular parallel graph coloring algorithm has been used to color the Jacobian. However, this parallel graph coloring algorithm shows poor scalability in parallel. The coloring numbers will increase with the processors, resulting in poor Jacobian computational efficiency.In this paper, a more efficient parallel graph coloring method is proposed that aims to reduce the coloring numbers and improve Jacobian computation efficiency in parallel. The main feature of the new method is that the coloring numbers decrease with the increasing number of processors. A neutronics/thermal-hydraulic coupling problem arising from the simplified high-temperature gas coolant model is utilized to assess the performance of the newly proposed method. The results show that (1) the parallel coloring number is reduced significantly, (2) the Jacobian computed by the new method is completely correct and excellent parallel scalability is achieved, and (3) the parallel coloring Newton-Krylov method with explicit Jacobian is more efficient and more stable than the parallel JFNK due to a better preconditioner. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the potentiality of the code HOFiD_bvp based on high order finite difference, following the approach of the boundary value methods and the upwind methods. Strategies, as variable stepsize and variable order, that helps to handle with solutions of singular perturbation problems, so as the continuation strategy applied for solving nonlinear problems, will be discussed. Now, the method is suitable to solve second order scalar boundary value problems, not only singularly perturbed with one and two parameters, but also problems with discontinuous source terms. Concerning that point some numerical tests will be taken in consideration in order to show the potentiality of the code. [ABSTRACT FROM AUTHOR]

We have developed a numerical scheme for the second‐order acoustic wave equation based on the Lie product formula and Taylor‐series expansion. The scheme has been derived from the analytical solution of the wave equation and in the approximation of the time derivative for a wavefield. Through these two equations, we obtained the first‐order differential equation in time, where the time evolution operator of the analytic solution of this differential equation is written as a product of exponential matrices. The new numerical solution using a Lie product formula may be combined with Taylor‐series, Chebyshev, Hermite and Legendre polynomial expansion or any other expansion for the cosine function. We use the proposed scheme combined with the second‐ or fourth‐order Taylor approximations to propagate the wavefields in a recursive procedure, in a stable manner, accurately and efficiently with even larger time steps than the conventional finite‐difference method. Moreover, our numerical scheme has provided results with the same quality as the rapid expansion method but requiring fewer computations of the Laplacian operator per time step. The numerical results have shown that the proposed scheme is efficient and accurate in seismic modelling, reverse time migration and least‐squares reverse time migration. [ABSTRACT FROM AUTHOR]

Induced polarization (IP) tomography measurements, as a near-surface geophysical method, can provide information about the degree of chargeability of subsurface materials and are commonly used in mineral exploration, engineering studies (e.g., sediment/bedrock interface identification, crushed zones and faults detection, and landslide and soil properties imaging), as well as in environmental investigations (contaminant plums identification and landfill characterization). The purpose of these measurements is to obtain the distribution of polarizability characteristics inside an object, generally below the surface, at the boundary of the object, or outside the area in question. The results of such measurements can be mathematically modeled for the specific polarizability properties by solving the Poisson’s equation restricted by appropriate boundary conditions. In this paper, we focused on the importance of simulating induced-polarization responses and retrieving chargeability distributions in geo-materials to enhance the characterization of subsurface structures. We presented the methods for forward modelling and non-linear inversion of IP measurements. To this end, in the first step, the Poisson’s equation for a two-dimensional ground with an arbitrary distribution of conductivity is solved using the finite difference numerical method. In the next step, based on the existing relations between conductivity and chargeability (the Siegel’s formulation), the apparent IP response is calculated. Finally, we solved the non-linear chargeability inversion problem following a non-linear apparent resistivity inversion. This is achieved by imposing physical constraints to prevent the estimation of unrealistic model parameters, using a Newton-based optimization method. To evaluate the efficiency of the proposed methodology, we utilized the proposed algorithm on two simulated examples and a real data set. Our numerical results show that the algorithm reliably represents the main features and structure of the Earth’s subsurface in terms of resistivity and chargeability models. All the algorithms presented in this paper have written in the MATLAB programming language. [ABSTRACT FROM AUTHOR]

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Mechanical ventilation is the primary measure for cooling during construction of high geo-temperature tunnel. Based on heat transfer theory and characteristics of press-in ventilation, a comprehensive calculation model considering the influence of construction process is proposed, and the reliability of the model is verified by on-site test. The effects of duct leakage rate and thermal conductivity of different excavation length on temperature field distribution during construction ventilation were analyzed based on the prediction model. The following conclusions are drawn: As the excavation length increases, the duct outlet temperature first increases and then decreases. The duct outlet temperature is mainly affected by geo-temperature and boundary control temperature of working face, the air leakage rate and excavation length are not the main factors. The highest temperature in the duct is about 40 °C. The distance between the position of highest temperature and working face increases with the increase of excavation length and decreases with the increase of air leakage rate. With the increase of excavation length, the impact of thermal conductivity on outlet temperature of duct is first enhanced and then stabilized under the same excavation length. The heat-insulated duct can effectively reduce the outlet air temperature and prolong the service life of the duct, while minimizing the air leakage of the duct.

Abstract This study presents a finite difference model for analyzing ground stability and settlement of twin circular culverts in undrained clay. The model is verified through simulations of soil movement and relaxation around a tunnel-boring machine's shield. Stability numbers and ground settlement are evaluated across various culvert geometries and soil ratios and compared to rigorous solutions and previous models. The settlement data obtained is used to determine inflection point parameters for practical culvert design, considering dimensionless ratios. The findings highlight the importance of precise design methodologies that consider soil properties and geometry. The finite difference model proves to be a valuable tool in culvert design, providing accurate analysis of stability and settlement characteristics. The presented design figures and regression equations serve as practical tools for engineers in designing stable twin circular culverts in undrained clay. The study emphasizes the need to carefully consider soil properties and geometry for successful culvert design. In conclusion, the finite difference model offers insights into ground stability and settlement of twin circular culverts. The presented design figures and regression equations support engineers in making informed design decisions, ensuring the stability and long-term performance of culverts in undrained clay conditions.

There are several large karst caves at haunch part of the Lidong Tunnel during construction, together with inrush water due to high pressure within these caves. In light of it, this paper takes YK342+113 section as an example and adopts finite difference software FLAC 3D, so as to analyze tunnel deformation when crossing karst caves under six different working conditions, including with or without karst cave, before and after karst treatment, along with support locations. According to analysis results: First, the wall rock mainly had deformation at tunnel vault when evacuating at the third bench, which is a critical monitoring focus for tunnel construction; Second, karst cave treatment contributed to better conduct forces on both sides of wall rock, thus reducing vault settlement, while not affecting horizontal convergence and upturn of vaults; Third, treatment measures were proved to be effective in minimizing wall rock deformation by comparing deformation curves under different conditions; Fourth, after treatment measures, the angular points within the cave’s chamber had stress concentration, which might cause secondary collapse. Field monitoring data revealed that the final settlement of the tunnel vault was relatively consistent with the numerical analysis results, with a distinct change in daily settlement after initial support construction. By integrating numerical analysis and field monitoring, the rationality of the karst treatment plan was fully verified, providing a valuable reference for similar projects.

In this paper, the MPI-based parallel library Free Molecular Dynamics (FMD) is introduced. The general structure of a typical program utilizing FMD to perform classical molecular dynamics (MD) simulation is described. Much of the paper is devoted to one of the advanced features of FMD: its ability to compute physical fields defined on distributed grids (a.k.a. “turies”). Each cell of a distributed grid may be shared among any number of MPI processes. Distributed grids can be used to combine MD with continuum models or to obtain macroscopic quantities, e.g. density, as functions of time and space. The library is designed to provide an easy to use interface for its users, as well as equip its developers with reusable tools required for expanding the code.

In this work, we study the numerical solution for time fractional Black-Scholes model under jump-diffusion involving a Caputo differential operator. For simplicity of the analysis, the model problem is converted into a time fractional partial integro-differential equation with a Fredholm integral operator. The L1 discretization is introduced on a graded mesh to approximate the temporal derivative. A second order central difference scheme is used to replace the spatial derivatives and the composite trapezoidal approximation is employed to discretize the integral part. The stability results for the proposed numerical scheme are derived with a sharp error estimation. A rigorous analysis proves that the optimal rate of convergence is obtained for a suitable choice of the grading parameter. Further, we introduce the Adomian decomposition method to find out an analytical approximate solution of the given model and the results are compared with the numerical solutions. The main advantage of the fully discretized numerical method is that it not only resolves the initial singularity occurred due to the presence of the fractional operator, but it also gives a higher rate of convergence compared to the uniform mesh. On the other hand, the Adomian decomposition method gives the analytical solution as well as a numerical approximation of the solution which does not involve any mesh discretization. Furthermore, the method does not require a large amount of computer memory and is free of rounding errors. Some experiments are performed for both methods and it is shown that the results agree well with the theoretical findings. In addition, the proposed schemes are investigated on numerous European option pricing jump-diffusion models such as Merton's jump-diffusion and Kou's jump-diffusion for both European call and put options. [ABSTRACT FROM AUTHOR]

The current effort is executed to interpret the heat transmission of combined stenosis and aneurysm in an artery, taking into account variable properties such as viscous dissipation and thermal radiation. We reduced the two directional energy and momentum equations to unidirectional flow by normalizing them under the mild stenotic assumption. After that, a mathematical framework for the physical problem is developed. An intricate nonlinear set of partial differential equations results from this formulation. A suitable numerical method of finite difference is employed on consequent equations to solve them. Afterward, graphical results predict the region of flow and the influence of involved parameters is shown in pictorial form. Furthermore, these solutions are employed to test how certain parameters, like streamlines, flow rate, and wall shear stress, affect blood flow. Using streamlines, we will also observe the general behavior of blood flow patterns. [ABSTRACT FROM AUTHOR]

Discrete-time Cohen–Grossberg neural networks (CGNNs) play important role in feedback neural networks. The existing literatures of CGNNs only regarded integral order discrete-time models without other variables. This paper builds the lattice model for nonlocal stochastic fuzzy CGNNs with reaction diffusions by employing the finite difference and Mittag–Leffler time Euler difference techniques. Further, the existence of a unique bounded almost automorphic sequence solution in distribution and global exponential convergence in the mean-square sense to the achieved difference model are investigated. At last, by using the tool of Matlab and time Euler difference for the Brownian motions, an illustrative example with simulations is used to show the feasible of the works of the current paper. We think that this work can contribute to achieve some effective real tasks, e.g. content-addressable memory, auto-association, dynamic reconstruction of a chaotic process, etc. [ABSTRACT FROM AUTHOR]