A higher-order accurate difference approximation of singularly perturbed reaction-diffusion problem using grid equidistribution

Abstract

This paper proposes a higher-order numerical approximation scheme to solve singularly perturbed reaction–diffusion boundary value problems. The proposed scheme is a combination of a fourth-order numerical difference method and classical central difference method applied on a non-equidistant grid. The non-equidistant grid is generated by equi-distributing a non-negative monitor function. The theoretical and empirical error analysis demonstrate that the proposed scheme has fourth-order uniform convergence with respect to the perturbation parameter.

Keywords

• Singular perturbation
• Boundary value problems
• Higher-order approximation
• Grid equidistribution
• Robust discretization
• Hybrid difference scheme