A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations

Po Wen Hsieh, Yin Tzer Shih, Suh Yuh Yang, Cheng Shu You

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish
Pages (from-to)1287-1301
Number of pages15
JournalCommunications in Computational Physics
Volume19
Issue number5
DOIs
StatePublished - 1 May 2016

Keywords

  • Il'in-Allen-Southwell scheme
  • System of singularly perturbed equations
  • boundary layer
  • formally second-order scheme
  • interior layer
  • system of viscous Burgers' equations

Fingerprint

Dive into the research topics of 'A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations'. Together they form a unique fingerprint.

Cite this