Higher-Order Numerical Scheme for Semi-linear Singularly Perturbed Reaction-Diffusion Problem

Abstract

In this paper, a higher-order numerical method presented for solving semi-linear singularly perturbed reaction-diffusion problems. The quasilinearization technique is used to linearize the semi-linear term. After uniform discertization of the solution domain the finite difference scheme is formulated. The stability and consistency are investigated to guarantee the convergence of the method. Further, numerical illustrations are provided to validate the applicability and efficiency of the proposed method. Moreover, the obtained results shows the betterment than some existing results in the literature.