A higher-order spline numerical method for a singularly perturbed reaction-diffusion boundary value problem

This work presents a new higher-order parameter-uniform spline numerical method for the solution of a singularly perturbed reaction-diffusion boundary value problem. A cubic spline in compression method on a modified Shishkin mesh is used to discretize the given singularly perturbed boundary value problem. The parameter-uniform convergence analysis of the present numerical method is well-established. The numerical method is theoretically almost fourth-order convergent. According to the computational results presented in the tables, the current method gives a higher-order numerical rate of convergence. The theoretical results are supported by two numerical examples.