A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations. (17th May 2016)

• Record Type: Journal Article
• Authors: Hsieh, Po-Wen; Shih, Yin-Tzer; Yang, Suh-Yuh; You, Cheng-Shu
• Is Part Of: Communications in computational physics. Volume 19:Number 5(2016:May)
• Page Start: 1287
• Page End: 1301
• Publication Date: 2016-05-17
• Subjects: 65N06, -- 65N12, -- 76M20; System of singularly perturbed equations, -- system of viscous Burgers' equations, -- boundary layer, -- interior layer, -- Il'in-Allen-Southwell scheme, -- formally second-order scheme; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.scpde14.21s
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: In this paper, we propose a novel and simple technique to construct effective difference schemes for solving systems of singularly perturbed convection-diffusion-reaction equations, whose solutions may display boundary or interior layers. We illustrate the technique by taking the Il'in-Allen-Southwell scheme for 1-D scalar equations as a basis to derive a formally second-order scheme for 1-D coupled systems and then extend the scheme to 2-D case by employing an alternating direction approach. Numerical examples are given to demonstrate the high performance of the obtained scheme on uniform meshes as well as piecewise-uniform Shishkin meshes.