Efficient computational method for singularly perturbed Burger-Huxley equations

Abstract

This paper focuses on an efficient computational method for solving the singularly perturbed Burger-Huxley equations. The difficulties encountered in solving this problem come from the nonlinearity term. The quasilinearization technique linearizes the nonlinear term in the differential equation. The finite difference approximation is formulated to approximate the derivatives in the differential equations and then accelerate its rate of convergence to improve the accuracy of the solution. The stability and consistency analysis were investigated to guarantee the convergence analysis of the formulated method. Numerical examples are considered for numerical illustrations. Numerical experiments were conducted to sustain the theoretical results and to show that the proposed method produces a more correct solution than some surviving methods in the literature.