Document Type : Research Paper
Pure and Applied Analytics Focus Area, North West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa
Pure and Applied Analytics Focus Area, School of Mathematical and Statistical Sciences, North West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa
In this paper, a one-dimensional modified Burgers' equation is considered for different Reynolds numbers. For very high Reynolds numbers, the solution possesses a multiscale character in some part of the independent domain and thus can be classified as a singularly perturbed problem. A numerical scheme that uses a fitted operator finite difference scheme to solve the spatial derivatives and the implicit Euler scheme for the time derivative is proposed to solve the modified Burgers' equation via Rothe's method. It is important to note that the proposed fitted operator finite difference scheme is based on the midpoint upwind scheme. The stability of the scheme is established and the error associated with each discretisation is estimated. Numerical simulations are carried out to validate the theoretical findings.