A numerical comparative study for the singularly perturbed nonlinear Volterra-Fredholm integro-differential equations on layer-adapted meshes

Abstract

This article deals with the singularly perturbed nonlinear Volterra-Fredholm integro-differential equations. Firstly, some priori bounds are presented. Then, the finite difference scheme is constructed on non-uniform mesh by using interpolating quadrature rules [5] and composite numerical integration formulas. The error estimates are derived in the discrete maximum norm. Finally, theoretical results are performed on two examples and they are compared for both Bakhvalov (B-type) and Shishkin (S-type) meshes.