Title of article :
A second order fitted operator finite difference scheme for a singularly perturbed degenerate parabolic problem
Author/Authors :
Adjoah Mbroh, Nana Pure and Applied Analytics Focus Area - North West University - Mafikeng Campus - Private Bag - Mmabatho, South Africa , Oukouomi Noutchie, Suares Clovis Pure and Applied Analytics Focus Area - North West University - Mafikeng Campus - Private Bag - Mmabatho, South Africa , M’pika Massoukou, Rodrigue Yves Pure and Applied Analytics Focus Area - North West University - Mafikeng Campus - Private Bag - Mmabatho, 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.
Keywords :
Singular perturbations , parabolic degenerate problem , fitted operator finite difference methods , convergence
Journal title :
International Journal of Nonlinear Analysis and Applications
