Uniformly convergent hybrid numerical scheme for singularly perturbed turning point problems with delay

Abstract

In the present work, we consider a class of singularly perturbed turning point problems with delay for their numerical solution. Due to the presence of a delay, there occurs an interior layer in the solution along with twin boundary layers (SIAM J. Appl. Math. 42(3): 502–530). Some a priori estimates are given on the exact solution and its derivatives. A numerical technique composed of hybrid finite difference scheme on a layer-adapted Shishkin mesh is proposed. We establish the consistency, stability and convergence of the proposed technique. To validate the theoretical predictions, we present some numerical illustrations. The proposed scheme is proved to have an almost second-order convergence rate, uniform with respect to the perturbation parameter ε.

Keywords:

• Turning point problem
• hybrid scheme
• singular perturbation
• piecewise-uniform Shishkin mesh
• delay differential equation

Mathematics Subject Classifications (2020):

• 65L11
• 65L12
• 65L20
• 65L50
• 65L70

Disclosure statement

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