Higher order numerical method for a class of singularly perturbed time dependent nonlinear reaction diffusion problems

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Document Type : Research Article

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Department of Mathematics, School of Engineering, Presidency University, Bengaluru - 560 064, Karnataka, India

Abstract

Nonlinear science plays an important role in modern technology. Because of the limitations over the linear theories and the chaotic nature of the problems in this technological era, investigation of nonlinear problems has become indispensable to analyse the dynamics of complicated and multi scale characteristics problems. This article aims at the analysis and implementation of a numerical method for a class of singularly perturbed time dependent nonlinear reaction diffusion problems. Together with classical finite difference operators, a piecewise uniform Shishkin mesh in the spatial direction and a uniform mesh in the temporal direction are used to formulate a new numerical method to solve the class of problems. The method is proved to be second order convergent in space and first order convergent in time uniformly with respect to the perturbation parameter. Numerical experiments are included which support the theoretical results.

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Journal of Mathematical Modeling

Articles in Press, Corrected Proof
Available Online from 21 November 2025

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