Uniformly convergent scheme for two-parameter singularly perturbed problems with non-smooth data

Abstract

A numerical scheme is constructed for the problems in which the diffusion and convection parameters (ϵ1 and ϵ2, respectively) both are small, and the convection and source terms have a jump discontinuity in the domain of consideration. Depending on the magnitude of the ratios urn:x-wiley:0749159X:media:num22553:num22553-math-0001, and urn:x-wiley:0749159X:media:num22553:num22553-math-0002 two different cases have been considered separately. Through rigorous analysis, the theoretical error bounds on the singular and regular components of the solution are obtained separately, which shows that in both cases the method is convergent uniformly irrespective of the size of the parameters ϵ1, ϵ2. Two test problems are included to validate the theoretical results.