Numerical Analysis for a weakly coupled system of Singularly Perturbed Quasilinear Problem with non-smooth data

This paper aims at solving a weakly coupled system of quasilinear convection diffusion equations with jump discontinuities in the convection and source terms. Due to the presence of a jump discontinuity in the convection term, the solution exhibits strong interior layers at the point of discontinuity. To approximate the solution of this problem, a hybrid difference technique is used and implemented on a Shishkin mesh. The proposed technique is proven to present an almost second order uniform convergence. To validate the theoretical results, some numerical examples are presented. • This article deals with a weakly coupled system of quasilinear convection diffusion equations with jump discontinuities in the convection and source terms. • Solutions to this kind of problems exhibit strong interior layers at the point of discontinuity, which makes them difficult to be solved numerically. • We have developed a hybrid difference technique implemented on a Shishkin mesh, showing an almost second order uniform convergence. • Comparisons with the standard upwind scheme show the best performance of the proposed approach.