Fitted numerical method for singularly perturbed Burger–Huxley equation

Abstract

Abstract This paper deals with the numerical treatment of a singularly perturbed unsteady Burger–Huxley equation. We linearize the problem using the Newton–Raphson–Kantorovich approximation method. We discretize the resulting linear problem using the implicit Euler method and specially fitted finite difference method for time and space variables, respectively. We provide the stability and convergence analysis of the method, which is first-order parameter uniform convergent. We present several model examples to illustrate the efficiency of the proposed method. The numerical results depict that the present method is more convergent than some methods available in the literature.

Keywords

• Singularly perturbed problems
• Burger–Huxley equation
• Implicit Euler method
• Fitted operator method
• Nonlinear problem