An Improved Numerical Scheme for Semilinear Singularly Perturbed Parabolic Delay Differential Equations

Abstract

This work proposes a more generalized numerical algorithm for delayed semilinear differential equations that are singularly perturbed in nature. After linearizing through the quasilinearization technique, a generalized θ-scheme is applied to deal with the time derivative term. The upwind scheme is applied to deal with the spatial derivative on layer resolving Shihskin type meshes which provides a uniform convergent result. The proposed scheme is also tested over a model with small space shifts (both negative and positive) and proved to be globally firstorder accurate. To illustrate the method’s efficiency, numerical results are verified through tables and figures.