Numerical treatment of singularly perturbed unsteady Burger-Huxley equation - Daba, Imiru Takele; Duressa, Gemechis File (Frontiers in Applied Mathematics and Statistics, 2023)
This paper deals with the numerical treatment of a singularly perturbed unsteady Burger-Huxley equation. The problem is linearized using the Newton-Raphson-Kantorovich approximation method. The resulting linear problem is discretized using the implicit Euler method and an exponential spline method for time and space variables, respectively. Richardson’s extrapolation technique is employed to increase the accuracy in the temporal direction. The stability and uniform convergence of the proposed scheme are investigated. The scheme is shown uniformly convergent with the order of convergence $O(τ +\ell^2)$ and $O(τ^2 +\ell^2)$ before and after Richardson extrapolation, respectively. Several test problems are considered to validate the applicability and efficiency of the scheme. It is observed that the proposed scheme provides more accurate results than the methods available in the literature.