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A fourth order optimal numerical approximation and its convergence for singularly perturbed time delayed parabolic problems

Publication Type : Journal Article

Publisher : Iranian Journal of Numerical Analysis and Optimization

Source : Iranian Journal of Numerical Analysis and Optimization

Campus : Coimbatore

School : School of Engineering

Center : Amrita Innovation & Research

Department : Mathematics

Verified : Yes

Year : 2021

Abstract : This paper presents a numerical solution for a time delay parabolic problem (reaction-diffusion) containing a small parameter. The numerical method combines the implicit Crank–Nicolson scheme for the time derivative on the uniform mesh and the central difference scheme for the spatial derivative on the Shishkin-type meshes. It is shown to be second-order uniformly convergent in time and space. Then Richardson extrapolation technique is applied to enhance the accuracy from second-order to fourth-order. The error analysis is carried out, and the method is proved to be uniformly convergent. These two methods are applied to two test examples in support of the theoretical results.

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