A Numerical Method for Singularly Perturbed Second Order Coupled System of Convection–Diffusion Robin Type Boundary Value Problems with Discontinuous Source Term

In this paper, a numerical method for a weakly coupled system of singularly perturbed convection–diffusion second order ordinary differential equations with discontinuous source term subject to Robin type boundary conditions is presented. A fitted mesh method has been used to obtain the difference scheme to solve the system of equations on a piecewise uniform Shishkin mesh. An error estimate is derived to show that the method is uniformly convergent with respect to singular perturbation parameter. Numerical results are provided to illustrate the theoretical results.