Fitted mesh method for singularly perturbed reaction-convection-diffusion problems with boundary and interior layers

被引：30
|
作者：
Shanthi V. [1 ]
Ramanujam N. [2 ]
Natesan S. [3 ]
机构：
[1] Department of Mathematics, School of Mathematics and Computer Science, Bharathidasan University, Tiruchirappalli 620 024, Tamilnadu
[2] Department of Mathematics, School of Mathematics and Computer Science, Bharathidasan University, Tiruchirappalli, Tamilnadu
[3] Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati - 781 039, Assam
来源：
Journal of Applied Mathematics and Computing | 2006年 / 22卷 / 1-2期
关键词：
Boundary and interior layers; Finite difference methods; Piecewise uniform meshes; Singular perturbation problems;
D O I：
10.1007/BF02896460
中图分类号：
学科分类号：
摘要：
A robust numerical method for a singularly perturbed second-order ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations. © 2006 Korean Society for Computational & Applied Mathematics and Korean SIGCAM.
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页码：49 / 65
页数：16
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