A Parameter-Uniform Essentially First Order Convergent Fitted Mesh Method for a Singularly Perturbed Robin Problem

janet Rajaiah; Valarmathi Sigamani

doi:https://doi.org/10.14445/22315373/IJMTT-V59P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 59 | Number 1 | Year 2018 | Article Id. IJMTT-V59P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V59P503

A Parameter-Uniform Essentially First Order Convergent Fitted Mesh Method for a Singularly Perturbed Robin Problem

janet Rajaiah, Valarmathi Sigamani

Citation :

janet Rajaiah, Valarmathi Sigamani, "A Parameter-Uniform Essentially First Order Convergent Fitted Mesh Method for a Singularly Perturbed Robin Problem," International Journal of Mathematics Trends and Technology (IJMTT), vol. 59, no. 1, pp. 8-21, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V59P503

Abstract

In this paper, a class of linear systems of singularly perturbed second order ordinary differential equations of reaction-diffusion type with Robin boundary conditions is considered. The components of the solution of this system exhibit boundary layers with sublayers. A piecewise-uniform Shishkin mesh is introduced and is used in conjunction with a classical finite difference discretisation, to construct a numerical method for solving this problem. It is proved that the numerical approximations obtained with this method are essentially first order convergent uniformly with respect to all of the parameters. Numerical illustration is provided to support the theory.

Keywords

Singular perturbations, boundary layers, system of differential equations, Robin boundary conditions, finite difference scheme, Shishkin meshes, parameter-uniform convergence

References

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