The Robust Numerical Schemes for Two-Dimensional Elliptical Singularly Perturbed Problems with Space Shifts

Abstract

AbstractThis 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 analyzed for convergence. The effect of shift terms on the solution behavior is demonstrated through numerical experiments. The paper concludes by providing several numerical results that demonstrate the performance of these three numerical schemes.Keywords: Singularly perturbed problemDifferential-difference equationsUpwind SchemeHybrid SchemeFitted operator finite-difference methodDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThe first author acknowledges the financial support received from the Council of Scientific and Industrial Research (File No.- 09/1112(0006)/2018-EMR-I) in the form of Senior Research Fellowship.Conflict of interestThe authors declare that they have no conflict of interest.