A parameter uniform fitted mesh method for a weakly coupled system of two singularly perturbed convection-diffusion equations
It provides a provably convergent numerical method for a specific class of boundary value problems, which is an incremental contribution to the field of singular perturbation problems.
The paper develops a numerical method for a system of two singularly perturbed convection-diffusion equations, proving first-order uniform convergence in the perturbation parameters with supporting numerical examples.
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.