High order ε-uniform methods for singularly perturbed reaction-diffusion problems with discontinuous coefficients and singular sources

We consider the reaction-diffusion equation with discontinues coefficients and singular sources in one dimension. In this work, we construct ε-uniformly convergent High Order Compact (HOC) monotone finite difference schemes defined on a priori Shishkin meshes, which have order two, three and four except for a logarithmic factor. Numerical experiments are presented and discussed.