A Monotone Hybrid Finite Difference Method For Singularly Perturbed Burgers’ Equation

Abstract

In this thesis, we deal with a monotone hybrid finite difference method for singularly perturbed Burgers’ equation. First, we apply quasilinearization process to tackle the non-linearity in the equation. We constructed a numerical scheme that comprises of an implicit second-order finite difference method to discretize the time derivative on uniform mesh and a monotone hybrid fi nite difference method to discretize the space derivative with piecewise uniform Shishkin mesh. The method has been shown to be second-order uniformly accurate in the time variable, and in the spatial direction it is first-order parameter uniform convergent in the outer region and almost second-order parameter uniform convergent in the boundary layer region. For small values of the parameter ε, a boundary layer is in the neighborhood of right part of the domain. Accuracy and uniform convergence of the proposed method is demonstrated by numerical experiments.