Fitted mesh numerical method for a coupled system of singularly perturbed reaction-diffusion robin boundary value problem having boundary and internal layers

In the present paper, Robin boundary value problem for a system of singularly perturbed reaction-diffusion equations with discontinuous source term is studied. The highest order derivative in each equation is multiplied by the perturbation parameters which are different in magnitude. The considered system does not obey maximum principle. Forward-backward approximation is used for the Robin boundary conditions and a central finite difference approximation is proposed for the differential system in conjunction with piecewise uniform Shishkin meshes and graded Bakhvalov meshes. The scheme is proved to be an almost first-order parameter uniform convergent. Numerical experiments are presented which are in line with the theoretical findings.