A Higher-Order New Approach Numerical Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems

Abstract

In this study, a higher-order new approach numerical method for solving singularly perturbed parabolic reaction-diffusion problems has presented. To discretize time variable, we used the Crank-Nicolson method on uniform mesh and space variable, we used hybrid numerical method comprising a cubic spline tension method in the inner regions and a central difference method in the outer region on Shishkin mesh. The proposed method is proved to be uniformly convergent irrespective of the perturbation parameter. Three numerical examples are computed to validate the theoretical findings.