Higher order numerical method for a semilinear system of singularly perturbed differential equations

In this paper, a system of singularly perturbed second order semilinear differential equations with prescribed boundary conditions is considered. To solve this problem, a parameter-uniform numerical method is constructed which consists of a classical finite difference scheme and a piecewise uniform Shishkin mesh. It is proved that the convergence of the proposed numerical method is essentially second order in the maximum norm. Numerical illustration presented supports the proved theoretical results