Parameter-uniform convergence of a numerical method for a coupled system of singularly perturbed semilinear reaction–diffusion equations with boundary and interior layers

Abstract

In this paper, we consider a coupled system of m ( ≥ 2 ) singularly perturbed semilinear reaction–diffusion equations with a discontinuous source term having a discontinuity at a point in the interior of the domain. The diffusion term of each equation is multiplied by small singular perturbation parameter, but these parameters are assumed to be different in magnitude. A numerical method is constructed on a variant of Shishkin mesh. The approximations generated by this method are shown to be almost second order uniformly convergent with respect to all perturbation parameters. Numerical results are in support of the theoretical results. • A coupled system of m ( ≥ 2 ) singularly perturbed semilinear reaction-diffusion equations is considered. • The source term is having a discontinuity at a point in the interior of the domain. • The diffusion term of each equation is multiplied by a small perturbation parameter. • All the perturbation parameters are different in magnitude. • The constructed numerical method has almost second parameter uniform convergence.