A higher order compact numerical approach for singularly perturbed parabolic problem with retarded term

Abstract

In this work, a compact finite difference approach is constructed for singularly perturbed parabolic reaction diffusion problems with a retarded term. The time and space derivatives have been discretized using the θ-method and a compact fourth-order finite difference method on a Shishkin mesh, respectively. Parameter uniform error estimates have been calculated in the $L_{\mathrm{\infty }}$ norm. Some numerical examples have been considered to corroborate the theoretical results and compare the numerical results with existing methods in the literature. It is shown that the present approach provides improved results till date for the problem considered in this paper.

Keywords:

• Shishkin mesh
• singularly perturbed problem
• uniform convergence
• θ-method
• compact finite difference
• delay differential equation

Mathematics Subject Classifications:

• 65L11
• 65M12
• 35K20

Disclosure statement

No potential conflict of interest was reported by the author(s).