HIGHER-ORDER PARAMETER UNIFORM CONVERGENT SCHEMES FOR ROBIN TYPE REACTION-DIFFUSION PROBLEMS USING ADAPTIVELY GENERATED GRID

Abstract

In this article, a singularly perturbed reaction-diffusion problem with Robin boundary conditions, is considered. In general, the solution of this problem possesses boundary layers at both the ends of the domain. To solve this problem, we propose a numerical scheme, involving the cubic spline scheme for boundary conditions and the classical central difference scheme for the differential equation (DE) at the interior points. The grid is generated by the equidistribution of a positive monitor function. It has been proved that classical forward–backward approximation for mixed type boundary conditions, gives first-order convergence, whereas our proposed cubic spline scheme provides second-order accuracy independent of the perturbation parameter. Numerical experiments have been provided to validate the theoretical results.