Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction-diffusion problems.

Abstract

<h4>Objective</h4>The main purpose of this work is to present a fourth-order fitted mesh scheme for solving the semilinear singularly perturbed reaction-diffusion problem to produce more accurate solutions.<h4>Results</h4>Quasilinearization technique is used to linearize the semilinear term. The scheme is formulated with discretizing the solution domain piecewise uniformly and then replacing the differential equation by finite difference approximations. This gives the system of difference algebraic equations and is solved by the Thomas algorithm. Convergence analysis are investigated using solution bound and the truncation error bound. Numerical illustrations are investigated to support the theoretical results and the method's applicability. The method produces a more accurate solution than some existing methods in the literature.