An adaptive difference scheme for parabolic delay differential equation with discontinuous coefficients and interior layers

Abstract

A class of singularly perturbed parabolic delay differential equation with discontinuous data is solved numerically. Numerical scheme based on the upwind finite difference method is presented on a specially generated mesh. The proposed numerical method has been analysed for consistency, stability, and convergence. It is found that the method proposed is unconditionally stable, and the convergence obtained is parameter uniform. Numerical illustrations are presented to demonstrate the effectiveness of the technique.