Mixed finite difference method for singularly perturbed differential difference equations with mixed shifts via domain decomposition

Abstract

In this paper, a mixed finite difference method is proposed to solve singularly perturbed differential difference equations with mixed shifts, solutions of which exhibit boundary layer behaviour at the left end of the interval using domain decomposition. A terminal boundary point is introduced into the domain, to decompose it into inner and outer regions. The original problem is reduced to an asymptotically equivalent singular perturbation problem and with the terminal point the singular perturbation problem is treated as inner region and outer region problems separately. The outer region and the modified inner region problems are solved by mixed finite difference method. The method is repeated for various choices of the terminal point. To validate the computational efficiency of the method model examples have been solved for different values of perturbation, delay and advanced parameters. Convergence of the proposed scheme has also been investigated.