Parameter-uniform fitted operator method for singularly perturbed Burgers-Huxley equation

Document Type : Research Article


1 Department of Mathematics, Adama Science and Technology University, Adama, Ethiopia

2 Department of Mathematics and Applied Mathematics, University of the Western Cape, Private BagX17, Bellville 7535, South Africa


We develop a robust uniformly convergent numerical scheme for singularly perturbed time dependent Burgers-Huxley partial differential equation. We first discretize the time derivative of the equation using the Crank-Nicolson finite difference method. Then, the resulting semi-discretized nonlinear ordinary differential equations are linearized using the quasilinearization technique, and finally, design a fitted operator upwind finite difference method to resolve the layer behavior of the solution in the spatial direction. Our analysis has shown that the presented method is second order parameter uniform convergent in time and first order in space. Numerical experiments are conducted to validate the theoretical results.