A uniformly convergent upwind scheme on harmonic mesh for singularly perturbed turning point problems

Abstract

In this article, a class of singularly perturbed turning point problems having two boundary layers is considered. The design and analysis of the upwind scheme on an a priori harmonic mesh ($H(\ell )$) for the considered class of problems is presented. The proposed numerical scheme is proved to be parameter uniformly convergent and of first order. Numerical experiments are performed to support the theoretical results and the efficiency of the proposed method is demonstrated by comparing with the upwind scheme on other existing meshes in the literature namely, B-mesh, Shishkin mesh and generalized Shishkin mesh.

Keywords:

• Singular perturbation problem
• turning point
• twin boundary layers
• harmonic mesh
• upwind scheme

AMS CLASSIFICATION:

• 65L11
• 65L12
• 34E20

Disclosure statement

No potential conflict of interest was reported by the authors.