UNIFORMLY CONVERGENT NUMERICAL METHOD FOR A SYSTEM OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS EXHIBITING BOUNDARY LAYERS

We study a system of singularly perturbed nonlinear Volterra integro-differential equations. The leading term of each equation is multiplied by a small positive parameter whose magnitude may vary. The presence of these parameters creates interacting and overlapping boundary layers in the solution. To resolve the issue of boundary layers, the piecewise uniform Shishkin mesh and the Bakhvalov-Shishkin mesh is formed. On these meshes, an upwind scheme for the derivative part along with the left rectangular rule for the integral part proves to be almost first order convergent uniformly in both parameters. Further, a post-processing technique is employed that improves the order of accuracy to second order. At the end, the theoretical findings are supported by a few numerical computations.