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In approximation theory, the "direct theorem" is a fundamental concept that relates to how well more straightforward functions or signals can approximate a function or signal from a chosen approximation space. The direct theorem typically provides bounds on the error or the quality of the approximation in terms of various parameters, such as the degree of approximation, the dimension of the approximation space, and the properties of the approximated functions. The specific form of the direct theorem can vary depending on the context and the type of approximation being considered (e.g., polynomial approximation, Fourier series approximation, spline approximation, etc.). The direct theorem aims to establish the mathematical framework for comprehending how well elements from a given space can approximate a function, which is crucial in various fields like numerical analysis, signal processing, and scientific computing. Finally, the direct theorem is a crucial result in approximation theory. It describes how elements from a given approximation space get closer and better at approximating a given function as the number of terms in the approximation sequence grows. It provides essential insights into the behavior of approximations and plays a central role in various mathematical and computational disciplines. In this article, we aim to prove the direct theorem by defining a new appropriate operator for functions Lp ([[0, 2π]d) that uses our new k-mixed modulus of smoothness to estimate the best approximation degree and the new k-mixed difference. Also, to prove the direct theorem, we introduce the angular approximation in Lp ([0, 2π]d to reach the most accurate estimate. [ABSTRACT FROM AUTHOR]

In this paper, Computing the eigenvalues of the Conformable Sturm-Liouville Problem (CSLP) of order 2α, 1/2 < α; ≤ 1, and dirichlet boundary conditions is considered. For this aim, CSLP is discretized to obtain a matrix eigenvalue problem (MEP) using finite element method with fractional shape functions. Then by a method based on the asymptotic form of the eigenvalues, we correct the eigenvalues of MEP to obtain efficient approximations for the eigenvalues of CSLP. Finally, some numerical examples to show the efficiency of the proposed method are given. Numerical results show that for the nth eigenvalue, the correction technique reduces the error order from O(n4h²) to O(n²h²). [ABSTRACT FROM AUTHOR]

The variational iteration technique (VIT) is an excellent analytical tool employed in this study to solve the nonlinear 3D-fractional differential equations. The Antagana-Baleanu sense is used to characterize the fractional derivatives (ABFD). To show the applicability of the recommended technique, example is presented. [ABSTRACT FROM AUTHOR]

In this manuscript, we present and test a numerical scheme with an algorithm to solve Volterra and Abel's integral equations utilizing generalized sampling operators. Illustrative computational examples are included to indicate the validity and practicability of the proposed technique. All of the computational examples in this research have been computed on a personal computer implementing some programs coded in MATLAB. [ABSTRACT FROM AUTHOR]

Copyright of International Journal of Engineering Research & Development (IJERAD) is the property of International Journal of Engineering Research & Development 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.)

If the matrix function f (A t) posses the properties of f (A t) = g f (t k A , then the recurrence formula f i − 1 = g f i , i = N , N − 1 , ⋯ , 1 , f (t A) = f 0 , can be established. Here, f N = f (A N) = ∑ j = 0 m a j A N j , A N = t k N A . This provides an algorithm for computing the matrix function f (A t) . By specifying the calculation accuracy p, a method is presented to determine m and N in a way that minimizes the time of the above algorithm, thus providing a fast algorithm for f (A t) . It is important to note that m only depends on the calculation accuracy p and is independent of the matrix A and t. Therefore, f (A N) has a fixed calculation format that is easily computed. On the other hand, N depends not only on A, but also on t. This provides a means to select t such that N is equal to 0, a property of significance. In summary, the algorithm proposed in this article enables users to establish a desired level of accuracy and then utilize it to select the appropriate values for m and N to minimize computation time. This approach ensures that both accuracy and efficiency are addressed concurrently. We develop a general algorithm, then apply it to the exponential, trigonometric, and logarithmic matrix functions, and compare the performance with that of the internal system functions of Mathematica and Pade approximation. In the last section, an example is provided to illustrate the rapid computation of numerical solutions for linear differential equations. [ABSTRACT FROM AUTHOR]

We analyze the recently introduced family of preconditioners in [M. M. Rana et al., SIAM J. Sci. Comput., 43 (2021), pp. S475-S495] for the stage equations of implicit Runge--Kutta methods for s-stage methods. We simplify the formulas for the eigenvalues and eigenvectors of the preconditioned systems for a general s-stage method and use these to obtain convergence rate estimates for preconditioned GMRES for some common choices of the implicit Runge-Kutta methods. This analysis is based on understanding the inherent matrix structure of these problems and exploiting it to qualitatively predict and explain the main observed features of the GMRES convergence behavior, using tools from approximation and potential theory based on Schwarz--Christoffel maps for curves and close, connected domains in the complex plane. We illustrate our analysis with numerical experiments showing very close correspondence of the estimates and the observed behavior, suggesting the analysis reliably captures the essence of these preconditioners. [ABSTRACT FROM AUTHOR]

A pressure-robust stabilizer-free weak Galerkin (WG) finite element method has been defined for the Stokes equations on triangular and tetrahedral meshes. We have obtained pressure-independent error estimates for the velocity without any velocity reconstruction. The optimal-order convergence for the velocity of the WG approximation has been proved for the L 2 norm and the H 1 norm. The optimal-order error convergence has been proved for the pressure in the L 2 norm. The theory has been validated by performing some numerical tests on triangular and tetrahedral meshes. [ABSTRACT FROM AUTHOR]

A numerical-analytical solution of a problem concerning the current distribution and input characteristics of asymmetric biconical dipole with distributed surface impedance and arbitrary excitation and derived in the thin-wire approximation. Solution correctness is confirmed by satisfactory agreement of numerical and experimental results from literary sources. Numerical results are given for the input characteristics of the dipole in the case of its asymmetric excitation by a point source. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mathematics, Mechanics & Computer Science is the property of Al-Farabi Kazakh National University 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.)

Wormhole solutions in General Relativity (GR) require exotic matter sources that violate the null energy condition (NEC), and it is well-known that higher-order modifications of GR and some alternative matter sources can support wormholes. In this study, we explore the possibility of formulating traversable wormholes in f(R) modified gravity, which is perhaps the most widely discussed modification of GR, with two approaches. First, to investigate the effects of geometrical constraints on the global characteristics, we gauge the TT-component of the metric tensor and employ Padè approximation to check whether a well-constrained shape function can be formulated in this manner. We then derive the field equations with a background of string cloud and numerically analyse the energy conditions, stability, and amount of exotic matter in this space-time. Next, as an alternative source in a simple f(R) gravity model, we use the background cloud of strings to estimate the wormhole shape function and analyse the relevant properties of the space-time. These results are then compared with those of wormholes threaded by normal matter in the simple f(R) gravity model considered. The results demonstrate that string cloud is a viable source for wormholes with NEC violations; however, the wormhole space-times in the simple f(R) gravity model considered in this study are unstable. [ABSTRACT FROM AUTHOR]

In this paper, we focus on investigating a post-processing technique designed for one-dimensional singularly perturbed parabolic convection-diffusion problems that demonstrate a regular boundary layer. We use a backward Euler numerical approach for time derivatives with uniform mesh in the temporal direction, and a simple upwind scheme is used for spatial derivatives with modified graded mesh in the spatial direction. In this study, we demonstrate the effectiveness of the Richardson extrapolation technique in enhancing the ε-uniform accuracy of simple upwinding within the discrete supremum norm, as evidenced by an improvement from O(N-1 ln(1/ε) +Δθ) to O(N-2 ln²(1/ε) +Δθ²). Furthermore, to validate the theoretical findings, computational experiments are conducted for two test examples by applying the proposed technique. [ABSTRACT FROM AUTHOR]

This article presents a novel numerical approach to the solution of the nonlinear Kawahara equation. The desired approximations are obtained from the combination of Dickson polynomials and Taylor's expansion. The combined approach is based on Taylor's expansion for discretizing the time derivative and Dickson polynomials for space derivatives. The problem will be converted into a system of linear algebraic equations for each time step via some suitable collocation points. Error estimation is presented after obtaining the approximate solution. The newly proposed technique is compared with some existing numerical methods to show the method's applicability, accuracy, and efficacy. Two problems are solved to demonstrate the method's power and effect, and the results are presented as a table and graphics. [ABSTRACT FROM AUTHOR]

Ratio product estimators have been proposed by several authors for the estimation of the population mean and population variance, but very few authors have proposed ratio product estimators for the estimation of the population coefficient of variation. In this paper, we propose a ratio product estimator for the estimation of the population coefficient of variation. The mean square error of the proposed estimator was obtained up to the first order of approximation using the Taylor series technique. A numerical analysis was conducted, and the results show that the proposed ratio product estimator is more efficient. [ABSTRACT FROM AUTHOR]

We revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons with curved edges. In the second part of the paper, we introduce a couple of new ideas for the construction of Virtual Element Method (VEM)-approximations on domains with curved boundary, both in two and three dimensions. The new approach looks promising, although sound numerical tests should be made to validate the efficiency of the method. [ABSTRACT FROM AUTHOR]

In this article, we construct a new sequence of Sz'asz-Mirakjan-Kantorovich operators denoted as Kn;g (f; x), which depending on a parameter g. We prove direct and local approximation properties of Kn;g (f; x). We obtain that, if g > 1, then the operators Kn;g (f; x) provide better approximation results than classical case for all x 2 [0;¥). Furthermore, we investigate the approximation results of Kn;g (f; x), graphically and numerically. Moreover, we introduce new operators from Kn;g (f; x) that preserve affine functions and bivariate case of Kn;g (f; x). Then, we study their approximation properties and also illustrate the convergence of these operators comparing with their classical cases. [ABSTRACT FROM AUTHOR]

The aim of this article is to present a new method based on Lucas polynomials and residual error function for a numerical solution of fractional Bagley–Torvik equations. Here, the approximate solution is expanded as a linear combination of Lucas polynomials, and by using the collocation method, the original problem is reduced to a system of linear equations. So, the approximate solution to the problem could be found by solving this system. Then, by using the residual error function and approximating the error function by utilizing the same approach, we achieve more accurate results. In addition, the convergence analysis of the method is investigated. Numerical examples demonstrate the validity and applicability of the method. [ABSTRACT FROM AUTHOR]

This paper is interested in studying the one-phase Stefan problem. For this purpose, we use the nonlinear sentinel method, which relies typically on the approximate controllability and the Fanchel-Rockafellar duality of the minimization problem, to prove the existence and uniqueness of a solution to this problem. In particular, our research focuses on the application of the nonlinear sentinel method to the single-phase Stefan problem. This approach aids in identifying an unspecified boundary section within the domain undergoing a liquid-solid phase transition. We track the evolution of the temperature profile in the liquid-solid material and the corresponding movement of its interface over time. Eventually, the local convergence used for the iterative numerical scheme is demonstrated. [ABSTRACT FROM AUTHOR]

In the current study, a new numerical algorithm is presented to solve a class of nonlinear fractional integral-differential equations with weakly singular kernels. Cubic hat functions (CHFs) and their properties are introduced for the first time. A new fractional-order operational matrix of integration via CHFs is presented. Utilizing the operational matrices of CHFs, the main problem is transformed into a number of trivariate polynomial equations. Error analysis and the convergence of the proposed method are evaluated, and the convergence rate is addressed. Ultimately, three examples are provided to illustrate the precision and capabilities of this algorithm. The numerical results are presented in some tables and figures. [ABSTRACT FROM AUTHOR]

In almost all fields of numerical analysis, spline functions are the most effective tool for polynomials employed as the fundamental method of approximation theory. Additionally, existence, uniqueness, and error boundaries are required for the spline creation in the g-spline interpolation issue. Mathematics, physics, biology, engineering, signal processing, systems identification, control theory, finance, and fractional dynamics have all shown an interest in fractional differential equations, also work in social sciences including economics, finance, and dietary supplements. It is crucial to find both close and accurate solutions of fractional differential equations. To find solutions of fractional differential equations, several analytical and numerical techniques have been developed. In this paper, we extend the five-degree spline (0,4) lacunary interpolation on uniform meshes. The outcomes, uniqueness and error boundaries for generalize (0,4) Lacunary interpolation using five- degree splines. These generalizes outperform the usage of the (0,4) five splines for interpolation. [ABSTRACT FROM AUTHOR]

We offer a new asymptotic expansion with an explicit remainder estimate in the central limit theorem. The results obtained are essentially based on new forms of asymptotic expansions in the central limit theorem. We also present a more accurate estimation of the CLT-expansions remainder which is rigorously proved and backed up numerically. It is shown that our approach can be used for further refinement of allied asymptotic expansions. [ABSTRACT FROM AUTHOR]

This paper establishes convergence rates and error estimates for the pseudo-polyharmonic div-curl and elastic interpolation. This type of interpolation is based on a combination of the divergence and the curl of a multivariate vector field and minimizing an appropriate functional energy related to the divergence and curl. Convergence rates and error estimates are established when the interpolated vector field is assumed to be in the classical fractional vectorial Sobolev space on an open bounded set with a Lipschitz-continuous boundary. The error estimates introduced in this work are sharp and the rate of convergence depends algebraically on the fill distance of the scattered data nodes. More precisely, the order of convergence depends, essentially, on the smoothness of the target vector field, on the dimension of the Euclidean space and on the null space of corresponding Sobolev semi-norm.

In this paper, a highly accurate method is introduced to achieve the numerical solution of the advection diffusion equation (ADE). This approach contains collocation technique based on nonic B-spline functions in the spatial-domain discretization and Adams Moulton scheme in the temporal-domain discretization. Two test problems are studied to validate effectiveness of the new presented method and efficiency of the approximate results are tested by calculating rate of temporal-convergence and error norm L8 for the suggested method. The obtained numerical results are compared in the tables by the other available studies in literature and it is observed that a better approximate solution is provided than the existing methods. [ABSTRACT FROM AUTHOR]

The present study focuses on the two new hybrid methods: variational iteration J-transform technique (J-VIT) and J-transform method with optimal homotopy analysis (OHAJTM) for analytical assessment of space-time fractional Fokker-Planck equations (STF-FPE), appearing in many realistic physical situations, e.g., in ultra-slow kinetics, Brownian motion of particles, anomalous diffusion, polymerases of Ribonucleic acid, deoxyribonucleic acid, continuous random movement, and formation of wave patterns. OHAJTM is developed via optimal homotopy analysis after implementing the properties of J-transform while (J-VIT) is produced by implementing properties of the J-transform and the theory of variational iteration. Banach approach is utilized to analyze the convergence of these methods. In addition, it is demonstrated that J-VIT is T-stable. Computed new approximations are reported as a closed form expression of the Mittag-Leffler function, and in addition, the effectiveness/validity of the proposed new approximations is demonstrated via three test problems of STF-FPE by computing the error norms: L2 and absolute errors. The numerical assessment demonstrates that the developed techniques perform better for STF-FPE and for a given iteration, and OHAJTM produces new approximations with better accuracy as compared to J-VIT as well as the techniques developed recently. [ABSTRACT FROM AUTHOR]

In this paper, a mixed finite element method combined with Crank-Nicolson scheme approximation of parabolic optimal control problems with control constraint is investigated. For the state and co-state, the order m = 1 Raviart-Thomas mixed finite element spaces and Crank-Nicolson scheme are used for space and time discretization, respectively. The variational discretization technique is used for the control variable. We derive optimal priori error estimates for the control, state and co-state. Some numerical examples are presented to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

In a recent work (Koc et al., SIAM J. Numer. Anal. 59(4), 2163–2196, 2021), the authors showed that including difference quotients (DQs) is necessary in order to prove optimal pointwise in time error bounds for proper orthogonal decomposition (POD) reduced order models of the heat equation. In this work, we introduce a new approach to including DQs in the POD procedure. Instead of computing the POD modes using all of the snapshot data and DQs, we only use the first snapshot along with all of the DQs and special POD weights. We show that this approach retains all of the numerical analysis benefits of the standard POD DQ approach, while using a POD data set that has approximately half the number of snapshots as the standard POD DQ approach, i.e., the new approach requires less computational effort. We illustrate our theoretical results with numerical experiments. [ABSTRACT FROM AUTHOR]

The problem of biasness and availability of auxiliary variable for the estimating population mean is a big concern, both can be handled by proposing unbiased estimators in the absence of auxiliary variable. So in this paper unbiased exponential type estimators of population mean have been proposed. The estimators are proposed in the absence of the instrumental variable called the auxiliary variable by taking the advantage of the population and the sample median of the study variable. To about the first order approximation, the theoretical formulations of the bias and mean square error (MSE) are obtained. The circumstances in which the suggested estimators have the lowest mean squared error values when compared to the existing estimators were also deduced. In comparison to the currently used estimators, it was discovered that the suggested estimators of population mean had the lowest MSE, hence highest efficiency. Also least influence from the data's influential observations when it came to accurately calculating the population mean for skewed data. The theoretical findings of the paper are validated by the numerical study. [ABSTRACT FROM AUTHOR]

We show that the Wynn recurrence (the missing identity of Frobenius of the Padé approximation theory) can be incorporated into the theory of integrable systems as a reduction of the discrete Schwarzian Kadomtsev–Petviashvili equation. This allows, in particular, to present the geometric meaning of the recurrence as a construction of the appropriately constrained quadrangular set of points. The interpretation is valid for a projective line over arbitrary skew field what motivates to consider non-commutative Padé theory. We transfer the corresponding elements, including the Frobenius identities, to the non-commutative level using the quasideterminants. Using an example of the characteristic series of the Fibonacci language we present an application of the theory to the regular languages. We introduce the non-commutative version of the discrete-time Toda lattice equations together with their integrability structure. Finally, we discuss application of the Wynn recurrence in a different context of the geometric theory of discrete analytic functions. [ABSTRACT FROM AUTHOR]

The steady‐state laminar nonisothermal, incompressible viscoelastic fluid flows with the Jeffrey model between two counterrotating (same direction) rolls are studied analytically. The Jeffrey model is reduced to the Newtonian model after some appropriate modifications. The new dimensionless governing equations are acquired through suitable nondimensional values. The lubrication approximation theory is employed for the simplification of emerging equations. The exact expressions for pressure gradient, velocity, temperature, and flow rate are accomplished whereas some quantities of interest such as pressure, coating thickness, power transmitted by rolls to the fluid, and roll separation force are computed numerically by using a numerical method. The influence of emerging parameters such as the ratio of relaxation time to the retardation time λ1 ${\lambda }_{1}$, magnetohydrodynamic (MHD) parameter M $M$ and Brinkman number Br $Br$ on velocity profile, temperature profile, pressure gradient, pressure distribution, coating thickness, power input, and force of roll separation are presented numerically in a tabular way and specific outcomes are demonstrated graphically. The MHD acts as a regulatory parameter for various quantities of important interest, such as velocity, coating thickness, and temperature. It is worth noting that the coating thickness decreases as modified capillaries number is increased. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm of inertial type for approximating solutions of split equality fixed point problems involving quasi-Φ-nonexpansive maps is proposed and studied in the setting of certain real Banach spaces. Weak and strong convergence theorems are proved under some conditions. Some applications of the theorems are presented. The results presented ex- tend and improve some existing results. Finally, some numerical illustrations are presented to support our theorems and their applications. [ABSTRACT FROM AUTHOR]

In this paper, some properties of linear functionals are studied, which are used in functional analysis, optimization theory, numerical analysis, approximation theory, various applications, etc. [ABSTRACT FROM AUTHOR]

The grade-added rough set (GRS) approach is an extension of the rough set theory proposed by Pawlak to deal with numerical data. However, the GRS has problems with overtraining, unclassified and unnatural results. In this study, we propose a new approach called the directional neighborhood rough set (DNRS) approach to solve the problems of the GRS. The information granules in the DNRS are based on reflexive and antisymmetric relations. Following these relations, new lower and upper approximations are defined. Based on these definitions, we developed a classifier with a three-step algorithm, including DN-lower approximation classification, DN-upper approximation classification, and exceptional processing. Three experiments were conducted using the University of California Irvine (UCI)'s machine learning dataset to demonstrate the effect of each step in the DNRS model, overcoming the problems of the GRS, and achieving more accurate classifiers. The results showed that when the number of dimensions is reduced and both the lower and upper approximation algorithms are used, the DNRS model is more efficient than when the number of dimensions is large. Additionally, it was shown that the DNRS solves the problems of the GRS and the DNRS model is as accurate as existing classifiers. [ABSTRACT FROM AUTHOR]

The transportation problem (TP) is a significant factor in operational research. Numerous researchers have put forth various solutions to these problems. The goal is to reduce the overall cost of distributing resources from multiple sources to numerous destinations. If there are road risks (snow, flood, etc.), traffic limitations, etc., it might not be feasible to transport products from one place to another. In these circumstances, the appropriate route(s) can be given an extremely high unit cost, such as M (or ∞). Following that, a specific case of the prohibited transportation problem is introduced. Therefore, the focus of this study is to provide a novel algorithm that will reduce the cost of restricted transportation problems. With a few modifications, the traditional Vogel approach has been enhanced. The proposed method would perform better than the other approaches now in use. The numerical problem is resolved to demonstrate the effectiveness of the proposed approach and make comparisons with different approaches already in use. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a numerical approach to solve a distributed order time fractional COVID 19 virus model. The fractional derivatives are shown in the Caputo-Prabhakar contains generalized Mittag-Leffler Kernel. The coronavirus 19 disease model has 8 Inger diets leading to system of 8 nonlinear ordinary differential equations in this sense, we used the midpoint quadrature method and finite different scheme for solving this problem, our approximation method reduce the distributed order time fractional COVID 19 virus equations to a system of algebraic equations. Finally, to confirm the efficiency and accuracy of this method, we presented some numerical experiments for several values of distributed order. Also, all parameters introduced in the given model are positive parameters. [ABSTRACT FROM AUTHOR]

We consider the spectral approximation of flow optimal control problems with state constraint. The main contribution of this work is to derive an a posteriori error estimator, and show the upper and lower bounds for the approximation error. Numerical experiment shows the efficiency of the error indicator, which will be used to construct reliable adaptive hp spectral element approximation for flow control in the future work. [ABSTRACT FROM AUTHOR]

This paper derives moment approximation as well as the mean and the variance of a money return model within an important diffusion return process by considering the stochastic analogs of classical differences and differential equations. This is accomplished by employing an interest rate process that follows a birth and death diffusion process with general external effect process and represented as a solution to a stochastic differential equation. The analysis introduces a generalization of a widely applied statistical distribution, the exponential distribution. In particular, the moment approximation for some external effect distributions of Beta and Exponential distributions, as well as for the case of no external effects are generated. Numerical examples for a sample path of such a money return process are also considered for the case of fixed annualized interest rate and for the case of no jumps as well as the case of the occurrence of jump process that follow a uniform and exponential distribution. The results are useful in studying the behavior of the process and in statistical inference problems. The model generalization should attract wider applicability. [ABSTRACT FROM AUTHOR]

We apply Henderson’s method for measuring the cavity distribution function y(r) [J. Henderson, Mol. Phys. 48, 389 (1983)] to obtain the pair distribution function at contact, g(σ+). In contrast to the conventional distance-histogram method, no approximate extrapolation to contact is required. The resulting equation of state from experiments and simulations of hard disks agrees well with the scaled particle theory prediction up to high fluid packing fractions. We also provide the first experimental measurement of y(r) inside the hard core, which will allow for a more complete comparison with theory. The method’s flexibility is further illustrated by measuring the partial pair distribution functions of binary hard-disk mixtures in simulation. The equation for the contact values can be used to derive familiar results from statistical geometry. [ABSTRACT FROM AUTHOR]

The advancement in numerical models of serious resistant illnesses is a key research territory in different fields including the nature and the study of disease transmission. One of the aims of these models is to comprehend the elements of conduction of these infections. For the new strain of Covid-19 (Coronavirus), there has been no immunization to protect individuals from the virus and to forestall its spread so far. All things being equal, control procedures related to medical services, for example, social distancing or separation, isolation, and travel limitations can be adjusted to control this pandemic. This article reveals some insights into the dynamic practices of nonlinear Coronavirus models dependent on the homotopy annoyance strategy (HPM). We summon a novel sign stream chart that is utilized to depict the Coronavirus model. Through the numerical investigations, it is uncovered that social separation of the possibly tainted people who might be conveying the infection and the healthy virus-free people can diminish or interrupt the spread of the infection. The mathematical simulation results are highly concurrent with the statistical forecasts. The free balance and dependability focus for the Coronavirus model is discussed and the presence of a consistently steady arrangement is demonstrated. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to find approximate solutions to the fractional telegraph differential equation (FTDE) using Laplace transform collocation method (LTCM). The equation is defined by Caputo fractional derivative. A new form of the trial function from the original equation is presented and unknown coefficients in the trial function are computed by using LTCM. Two different initial-boundary value problems are considered as the test problems and approximate solutions are compared with analytical solutions. Numerical results are presented by graphs and tables. From the obtained results, we observe that the method is accurate, effective, and useful. [ABSTRACT FROM AUTHOR]

A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under recent consideration is to enforce bounds constraints on the approximating polynomial. In this paper, we consider the problem of constructioning such approximations using polynomials in the Bernstein basis. We consider a family of inequality-constrained quadratic programs. In the univariate case, a quadratic cone constraint allows us to search over all nonnegative polynomials of a given degree. In both the univariate and multivariate cases, we consider approximate problems with linear inequality constraints. Additionally, our method can be modified slightly to include equality constraints such as mass preservation. [ABSTRACT FROM AUTHOR]

To solve the problems of curves and surfaces approximation with normalized totally positive bases, a new progressive and iterative approximation for least square fitting method called HSS-LSPIA is proposed, which is based on the HSS iterative approach for solving linear equations of LSPIA. The HSS-LSPIA format includes two iterations with iterative difference vectors, each of which is distinct from the other. The approximate optimal positive constant, as well as convergence analyses, are provided. Furthermore, the HSS-LSPIA method can be faster than the ELSPIA, LSPIA, and WHPIA methods in terms of convergence speed. Numerical results verify this phenomenon. [ABSTRACT FROM AUTHOR]

In this paper, a new approach is presented to investigate the time-fractional advectiondispersion equation that is extensively used to study transport processes. The present modified fractional derivative operator based on Atangana-Baleanu’s definition of a derivative in the Caputo sense involves singular and non-local kernels. A numerical approximation of this new modified fractional operator is provided and applied to an advection-dispersion equation. Through Fourier analysis, it has been proved that the proposed scheme is unconditionally stable. Numerical examples are solved that validate the theoretical results presented in this paper and ensure the proficiency of the numerical scheme. [ABSTRACT FROM AUTHOR]

A system of singularly perturbed initial value problems with weak constrained conditions on the coefficients is considered. First the system of second-order singularly perturbed problems is transformed into a system of first-order singularly perturbed problems with integral terms, which facilitates the subsequent stability and a posteriori error analyses. Then a hybrid difference method with the use of interpolating quadrature rules is utilized to approximate the transformed system. Next a posteriori error analysis for the discretization scheme on an arbitrary mesh is presented. A solution-adaptive algorithm based on a posteriori error estimation is devised to generate a posteriori mesh and obtain approximation solution. Finally numerical experiments show a uniform convergence behavior of second-order for the scheme, which improves the previous results and achieves the optimal convergence order under the given discrete scheme. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new schemes based on the global Hessenberg processes for computing approximate solutions to low-rank Sylvester tensor equations. We first construct bases for the matrix and extended matrix Krylov subspaces by applying the global and extended global Hessenberg processes. Then the initial problem is projected into the matrix or extended matrix Krylov subspaces with small dimensions. The reduced Sylvester tensor equation obtained by the projection methods can be solved by using a recursive blocked algorithm. Furthermore, we present the upper bounds for the residual tensors without requiring the computation of the approximate solutions in any iteration. Finally, we illustrate the performance of the proposed methods with some numerical examples. [ABSTRACT FROM AUTHOR]

Fuzzy Integral equations is a mathematical tool for modeling the uncertain control system and economic. In this paper, we present numerical solution of nonlinear fuzzy Volterra integral equations (NFVIEs) using successive approximations scheme and block-pulse functions. Additionally, the convergence analysis of the presented approach is investigated involving Lipschitz and several conditions and error bound between the approximate and the exact solution is provided. Finally, to approve the outcomes concerned with the theory a numerical experiment is considered. [ABSTRACT FROM AUTHOR]

Co-extruded multi-layer plastic sheets and polymer structures formed by calendering process or by cold rolling are widely used in the packaging industry and thin-film transistor manufacturing. The different materials are extruded from separate extruders into the single sheet die which delivers a multi-layer sheet with uniform layer thickness at die exit. This multi-layer sheet is then stretched between counter-rotating rolls to obtain final uniform multi-layer sheet. There are many factors which can influence this process. In this article, calendering a single layer Newtonian or Non-Newtonian material has been extended to analyze a two-layer calendering process for an incompressible Viscoplastic and Newtonian fluids as upper and lower layers with different viscosity ratios. To simplify the equations of motion, the lubrication approximation theory is used. The expressions of non-dimensional pressure gradient, pressure and velocity distribution of both layers are obtained analytically by using proper no slip boundary conditions and dimensionless variables. The dimensionless detachment point is approximated by Regula-Falsi (false position) method. The important engineering factors including detachment point, calendered sheet thickness, roll separation force, power input by rolls, torque on each roll, and adiabatic temperature are all computed. In addition, how the viscosity ratios and viscoplastic casson parameter affect these factors have been investigated. Moreover all established results in literature for single layer calendering Newtonian fluids are also validated at casson parameter β tending towards infinity. [ABSTRACT FROM AUTHOR]

Copyright of Journal of University of Anbar for Pure Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) 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.)

Purpose – This paper evaluates an alternative queuing concept for marine container terminals that utilize a truck appointment system (TAS). Instead of having all lanes providing service to trucks with appointments, this study considers the case where walk-in lanes are provided to serve those trucks with no appointments or trucks with appointments but arrived late due to traffic congestion. Design/methodology/approach – To enable the analysis of the proposed alternative queuing strategy, the queuing system is shown mathematically to be stationary. Due to the complexity of the model, a discrete event simulation (DES) model is used to obtain the average waiting number of trucks per lane for both types of service lanes: TAS-lanes and walk-in lanes. Findings – The numerical experiment results indicated that the considered queuing strategy is most beneficial when the utilization of the TAS lanes is expected to be much higher than that of the walk-in lanes. Originality/value – The novelty of this study is that it examines the scenario where trucks with appointments switch to the walk-in lanes upon arrival if the TAS-lane server is occupied and the walk-in lane server is not occupied. This queuing strategy/policy could reduce the average waiting time of trucks at marine container terminals. Approximation equations are provided to assist practitioners calculate the average truck queue length and the average truck queuing time for this type of queuing system. [ABSTRACT FROM AUTHOR]