Original scientific paper
A parameter uniform fitted mesh method for a weakly coupled system of two singularly perturbed convection-diffusion equations
Saravana Sankar Kalaiselvan
John J.H. Miller
Valarmathi Sigamani
Abstract
In this paper, a boundary value problem for a singularly perturbed linear system of two second order ordinary differential equations of convection-diffusion type is considered on the interval [0, 1]. The components of the solution of this system exhibit boundary layers at 0. A numerical method composed of an upwind finite difference scheme applied on a piecewise uniform Shishkin mesh is suggested to solve the problem. The method is proved to be first order convergent in the maximum norm uniformly in the perturbation parameters. Numerical examples are provided in support of the theory.
Keywords
Singular perturbation problems; System of convection-diffusion equations; Boundary layers; Shishkin mesh; Parameter uniform convergence
Hrčak ID:
227065
URI
Publication date:
25.10.2019.
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