Uniform Numerical Method For a Class of Parameterized Singularly Perturbed Problems

Abstract

In this paper, we consider a quasi-linear first order singularly perturbed boundary value problem depending on a parameter. The problem is discretized by a backward Euler finite difference scheme on an appropriate non-uniform mesh constructed adaptively by equidistributing a positive monitor function based on the solution. We show that the proposed method is first order convergent whose error constants are shown to be independent of the singular perturbation parameter. Further, the proposed method is extended to problems with mixed type boundary conditions. A numerical example is solved using the presented method to support the result of convergence proved theoretically.