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

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

Year:    2016

Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 1287–1301

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.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.scpde14.21s

Communications in Computational Physics, Vol. 19 (2016), Iss. 5 : pp. 1287–1301

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:   

  1. A high-order finite difference scheme for a singularly perturbed fourth-order ordinary differential equation

    Cen, Zhongdi | Xu, Aimin | Le, Anbo

    International Journal of Computer Mathematics, Vol. 95 (2018), Iss. 9 P.1806

    https://doi.org/10.1080/00207160.2017.1339869 [Citations: 4]
  2. A fast numerical method for solving coupled Burgers' equations

    Shi, Feng | Zheng, Haibiao | Cao, Yong | Li, Jingzhi | Zhao, Ren

    Numerical Methods for Partial Differential Equations, Vol. 33 (2017), Iss. 6 P.1823

    https://doi.org/10.1002/num.22160 [Citations: 14]
  3. Numerical Analysis of Singularly Perturbed System of Parabolic Convection–Diffusion Problem with Regular Boundary Layers

    Singh, Maneesh Kumar | Natesan, Srinivasan

    Differential Equations and Dynamical Systems, Vol. 30 (2022), Iss. 3 P.695

    https://doi.org/10.1007/s12591-019-00462-2 [Citations: 5]