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Mathematical Communications, Vol. 26 No. 1, 2021.

Original scientific paper

Higher order numerical method for a semilinear system of singularly perturbed differential equations

Manikandan Mariappan orcid id orcid.org/0000-0001-8268-7800 ; Department of Mathematics, Bharathidasan University, Tiruchirappalli - 620 024, Tamil Nadu, India
Ayyadurai Tamilselvan ; Department of Mathematics, Bharathidasan University, Tiruchirappalli - 620 024, Tamil Nadu, India

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Abstract

In this paper, a system of singularly perturbed second order semilinear differential equations with prescribed boundary conditions is considered. To solve this problem, a parameter-uniform numerical method is constructed which consists of a classical finite difference scheme and a piecewise uniform Shishkin mesh. It is proved that the convergence of the proposed numerical method is essentially second order in the maximum norm. Numerical illustration presented supports the proved theoretical results.

Keywords

Singular perturbation problems; Boundary layers; Semilinear differential equations; Finite difference scheme; Shishkin mesh; Parameter-uniform convergence

Hrčak ID:

252599

URI

https://hrcak.srce.hr/252599

Publication date:

10.3.2021.

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