Analysis of higher order difference method for a pseudo-parabolic equation with delay

WOS: 000504461100008In this paper, the author considers the one dimensional initial-boundary problem for a pseudo-parabolic equation with time delay in second spatial derivative. To solve this problem numerically, the author constructs higher order difference method and obtain the error estimate for its solution. Based on the method of energy estimates the fully discrete scheme is shown to be convergent of order four in space and of order two in time. Some numerical examples illustrate the convergence and effectiveness of the numerical method.Scientific and Technological Research Council of Turkey (TUBITAK)Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) [1059B191700821]This research was fully supported by Scientific and Technological Research Council of Turkey (TUBITAK) [grant number 1059B191700821]. The author would like to thank the Department of Mathematics of the University of Oklahoma for the hospitality during her work on the project, Nikola Petrov and Murad Ozaydin who were instrumental in arranging her stay in Oklahoma. Ilhame Amirali thanks Nikola Petrov for stimulating discussions

Uniform numerical approximation for parameter dependent singularly perturbed problem with integral boundary condition

WOS: 000441460300026In this paper, a parameter-uniform numerical method for a parameterized singularly perturbed ordinary differential equation containing integral boundary condition is studied. Asymptotic estimates on the solution and its derivatives are derived. A numerical algorithm based on upwind finite difference operator and an appropriate piecewise uniform mesh is constructed. Parameter-uniform error estimate for the numerical solution is established. Numerical results are presented, which illustrate the theoretical results

A RESENT SURVEY ON NUMERICAL METHODS FOR SOLVING SINGULARLY PERTURBED PROBLEMS

6th International Conference on Control and Optimization with Industrial Applications (COIA) -- JUL 11-13, 2018 -- Baku, AZERBAIJANWOS: 000463893800023…Minist Transport Commun & High Technologies Republ Azerbaijan, Baku State Univ, Inst Appl Mat

Three layer difference method for linear pseudo-parabolic equation with delay

This paper deals with the study a finite-difference approximation of the one dimensional initial-boundary value problem for a pseudo-parabolic equation containing time delay in second derivative. We propose three layer difference scheme and obtain the error estimates for its solution. Based on the method of energy estimates the fully discrete scheme is shown to be convergent of order four in space and order two in time. Numerical results are presented to illustrate the theoretical findings. (C) 2021 Elsevier B.V. All rights reserved.WOS:0006970298000062-s2.0-8511440298

A Second-Order Post-processing Technique for Singularly Perturbed Volterra Integro-differential Equations

In this paper, a singularly perturbed Volterra integro- differential equation is being surveyed. On a piecewise-uniform Shishkin mesh, a fitted mesh finite difference approach is applied using a composite trapezoidal rule in the case of integral component and a finite difference operator for the derivative component. The proposed technique acquires a uniform convergence in accordance with the perturbation parameter. To improve the accuracy of the computed solution, an extrapolation, specifically Richardson extrapolation, is used measured in the discrete maximum norm and almost second-order convergence is attained. Further numerical results are provided to assist the theoretical estimates.WOS:0006970795000012-s2.0-8511514782

A Second-Order Post-processing Technique for Singularly Perturbed Volterra Integro-differential Equations

In this paper, a singularly perturbed Volterra integro- differential equation is being surveyed. On a piecewise-uniform Shishkin mesh, a fitted mesh finite difference approach is applied using a composite trapezoidal rule in the case of integral component and a finite difference operator for the derivative component. The proposed technique acquires a uniform convergence in accordance with the perturbation parameter. To improve the accuracy of the computed solution, an extrapolation, specifically Richardson extrapolation, is used measured in the discrete maximum norm and almost second-order convergence is attained. Further numerical results are provided to assist the theoretical estimates.WOS:0006970795000012-s2.0-8511514782

A Fitted Second-Order Difference Method for a Parameterized Problem with Integral Boundary Condition Exhibiting Initial Layer

In this paper, the homogeneous type fitted difference scheme for solving singularly perturbed problem depending on a parameter with integral boundary condition is proposed. We prove that the method is O(N(-2)lnN) uniform convergent on Shishkin meshes. Numerical results are also presented.WOS:0006407763000012-s2.0-8510439956

A finite-difference method for a singularly perturbed delay integro-differential equation

KUDU, Mustafa/0000-0002-6610-0587WOS: 000381546600025We consider the singularly perturbed initial value problem for a linear first order Volterra integro-differential equation with delay. Our purpose is to construct and analyse a numerical method with uniform convergence in the perturbation parameter. The numerical solution of this problem is discretized using implicit difference rules for differential part and the composite numerical quadrature rules for integral part. On a layer adapted mesh error estimations for the approximate solution are established. Numerical examples supporting the theory are presented. (C) 2016 Elsevier B.V. All rights reserved

Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay

Yapman, Omer/0000-0003-3117-2932WOS: 000463302400022In this paper, the initial value problem for a quasilinear singularly perturbed delay Volterra integro-differential equation was considered. By the method of integral identities with the use of exponential basis functions and interpolating quadrature rules with the weight and remainder term in integral form, a fitted difference scheme is constructed and analysed. It is shown that the method displays first order uniform convergence in perturbation parameter. Some numerical results are given to confirm the theoretical analysis. (C) 2019 Elsevier B.V. All rights reserved

Stability inequalities for the delay pseudo-parabolic equations

This paper deals with the initial-boundary value problem for linear pseudo-parabolic equation. Using the method of energy estimates the stability bounds obtained for the considered problem. Illustrative example is also presented. © 2019 Academic Publications