A Fitted Mesh Numerical Method for Solving Singularly Perturbed Burger-Fisher Equation

Abstract

In this thesis, we presented a fitted mesh numerical method for solving singularly perturbed Burger- Fisher equation. Since the problem is nonlinear, we apply quasi-linearizion technique on the nonlinear part of the equation. Then, the resulting linearized problem is discretized using an implicit second-order finite difference approximation in the time direction on uniform mesh.The numerical scheme formulated using both forward and backward finite difference methods are applied in the space direction on a piecewise uniform Shishkin mesh.The error analysis has been established for the method. As a perturbation parameter goes to small values, a boundary layer is produced in the neighborhood of left lateral surface. Applicability of the proposed method is demonstrated by numerical experiments