Asymptotic and numerical methods for solving singularly perturbed differential difference equations with mixed shifts

Abstract

This article deals with an effcient approximation method named successive complementary expansion method (SCEM) for solving singularly perturbed differential-difference equations with mixed shifts. It is compared with the method of matched asymptotic expansion (MMAE) and the parameter uniform upwind finite difference scheme for solving such a model. The comparison shows, unlike the MMAE, the SCEM method requires no matching procedure. It requires less computation when compared to the upwind finite difference scheme on the Shishkin mesh. The error analysis is carried out to prove the robustness of the method. Some numerical experiments are provided, which show the effectiveness of the proposed method.

Keywords

• singular perturbation
• mixed shifts
• asymptotic expansion
• mmae
• scem
• upwind scheme