A second order fitted operator finite difference scheme for a singularly perturbed degenerate parabolic problem

Document Type : Research Paper

Authors

Pure and Applied Analytics Focus Area, North West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa

Abstract

A second order finite difference scheme is constructed to solve a singularly perturbed degenerate parabolic convection diffusion problem via Rothe's method. The solution of the problem exhibits a boundary layer on the left side of the spatial domain.  By means of the Crank Nicolson finite difference scheme, the time derivative is discretised to obtain a set of semi-discrete boundary value problems. Using a fitted operator finite difference scheme based on the midpoint downwind scheme,  the system of boundary value problems are discretized and analysed for convergence. Second order accuracy is established for each discretisation process. Numerical simulations are carried out to validate the theoretical error estimate.

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