Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations

Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown

A second order accurate method for a parameterized singularly perturbed problem with integral boundary condition

In this paper, we consider a class of parameterized singularly perturbed problems with integral boundary condition. A finite difference scheme of hybrid type with an appropriate Shishkin mesh is suggested to solve the problem. We prove that the method is of almost second order convergent in the discrete maximum norm. Numerical results are presented, which illustrate the theoretical results. © 2021 Elsevier B.V.2-s2.0-8511925117

Finite-difference method for parameterized singularly perturbed problem

We study uniform finite-difference method for solving first-order singularly perturbed boundary value problem (BVP) depending on a parameter. Uniform error estimates in the discrete maximum norm are obtained for the numerical solution. Numerical results support the theoretical analysis

Analysis of Difference Approximations to Delay Pseudo-Parabolic Equations

International Conference on Differential and Difference Equations and Applications (ICDDEA) -- MAY 18-22, 2015 -- Mil Acad, Amadora, PORTUGALWOS: 000391876600016This work deals with the one-dimensional initial-boundary Sobolev or pseudo-parabolic problem with delay. For solving this problem numerically, we construct fourth-order difference-differential scheme and obtain the error estimate for its solution. Further, for the time variable, we use the appropriate Runge-Kutta method for the realization of our differential-difference problem. Numerical results supporting the theory are presented