A fitted mesh method for a coupled semi-linear system of singularly perturbed initial value problems

Abstract

In this article, we analyzed a general system of first order singularly perturbed semi-linear equations with distinct perturbation parameters in the unit interval. As boundary layers are expected near the origin in the solution components, variants of piecewise uniform meshes, introduced by Shishkin, are constructed to discretize the unit interval and standard finite difference scheme is used to discretize the equations. Parameter uniform convergence of the composed numerical method is proved. A continuation method is used to compute the numerical solution of the non-linear problem and numerical illustrations are given in support.

Keywords:

• Singular perturbation problems
• system of semi-linear equations
• boundary layers
• Shishkin mesh
• parameter uniform convergence

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 65L11
• Secondary 65L12
• 65L50
• 65L70

Acknowledgment

The first author wishes to acknowledge the financial support extended through Dr. D.S. Kothari Post-Doctoral Fellowship (Award No. F.4-2/2006 (BSR)/MA/20-21/0064 dt: 14.09.2021) by the University Grants Commission, India, to carry out this research work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author has been supported with Dr. D. S. Kothari Postdoctoral Fellowship by the University Grants Commission, Government of India.