This paper introduces an accelerated uniformly convergent finite difference numerical approach for the singularly perturbed Burger-Huxley equation. The semi-linear property is treated with the help of the quasilinearization technique. A first-order finite difference approximation is applied in the temporal direction, and a nonstandard methodology of Mickens procedure is used in the spatial direction. To accelerate the rate of convergence from first to second-order, the Richardson extrapolation technique is applied. The convergence analysis of the proposed method has been established. Numerical experiments were conducted to support the theoretical results. Further, the result shows that the proposed method gives a more accurate solution than some existing methods in the literature.

In this paper, a higher-order uniformly convergent finite difference method is presented to solve one dimensional unsteady singularly perturbed Burger-Huxley equation. The quadratically convergent quasilinearization technique is used to linearize the nonlinear term of the equation under consideration. An upwind finite difference approximation is applied in the temporal direction, and a nonuniform Shishkin mesh type is used in the spatial direction. To accelerate the rate of convergence from first to second-order, the Richardson extrapolation technique is applied. The convergence analysis of the proposed method has been established. Finally, numerical experiments were conducted to support the theoretical results. Further, the result shows that the proposed method gives more accurate solution than some existing methods in the literature.