The robust numerical schemes for two-dimensional elliptical singularly perturbed problems with space shifts

ABSTRACT

This article focuses on the investigation of two-dimensional elliptic singularly perturbed problems that incorporate positive and negative shifts, the solution of this class of problems may demonstrate regular/parabolic/degenerate or interior boundary layers. The goal of this article is to establish the development of numerical techniques for two-dimensional elliptic singularly perturbed problems with positive and negative shifts having regular boundary layers. The three numerical schemes are proposed to estimate the solution of this class of problems based on the fitted operator and fitted mesh finite-difference methods. The fitted operator finite difference method is analysed for convergence. The effect of shift terms on the solution behaviour is demonstrated through numerical experiments. The paper concludes by providing several numerical results that demonstrate the performance of proposed numerical schemes.

KEYWORDS:

• Singularly perturbed problems
• differential-difference equations
• upwind scheme
• hybrid scheme
• fitted operator finite-difference method

MATHEMATIC SUBJECT CLASSIFICATIONS:

• 65N06
• 65N12
• 65N15
• 65N22

Acknowledgments

The authors would like to express great appreciation to anonymous reviewers for their valuable comments and suggestions, which have helped to improve the quality and presentation of this paper.

Disclosure statement

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

Additional information

Funding

This work was supported by Council of Scientific and Industrial Research, India [File No.-09/1112(0006)/2018-EMR-I] in the form of Senior Research Fellowship received by the first author.