Fourth-Order Finite Difference Scheme on Non-uniform Mesh for Semilinear Singularly Perturbed Reaction-Diffusion Problems

Abstract

In this thesis, fourth-order finite difference scheme on non-uniform mesh for semilinear singularly perturbed reaction-diffusion problem is presented. The quasilinearization technique is used to linearize the semilinear term. It is formulated by discretization of the solution domain and then replace the differential equation by finite difference approximation that gives the system of algebraic equation. The method is shown to be fourth-order convergent. Further, it is observed that the convergence is independent of the perturbation parameter. Numerical illustrations are investigated on some examples to support the theoretical results and the applicability of the method. Furthermore, the proposed method produces more accurate solution than some existing methods in the literature.