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A fourth-order numerical scheme for singularly perturbed delay parabolic problem arising in population dynamics

Publication Type : Journal Article

Publisher : Springer Berlin Heidelberg

Source : Springer Berlin Heidelberg

Campus : Coimbatore

School : School of Engineering

Center : Amrita Innovation & Research

Department : Mathematics

Verified : Yes

Year : 2020

Abstract : This article presents a higher-order parameter uniformly convergent method for a singularly perturbed delay parabolic reaction–diffusion initial-boundary-value problem. For the discretization of the time derivative, we use the implicit Euler scheme on the uniform mesh and for the spatial discretization, we use the central difference scheme on the Shishkin mesh, which provides a second-order convergence rate. To enhance the order of convergence, we apply the Richardson extrapolation technique. We prove that the proposed method converges uniformly with respect to the perturbation parameter and also attains almost fourth-order convergence rate. Finally, to support the theoretical results, we present some numerical experiments by using the proposed method

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