A seventh order numerical method for singular perturbation problems

doi:10.1016/j.amc.2006.08.022

2007-03-01

PRE

P. Pramod Chakravarthy *

K. Phaneendra

Y. N. Reddy

DOI：10.1016/j.amc.2006.08.022

原文链接

原文求助

摘要

En 中文

In this paper, a seventh order numerical method is presented for solving singularly perturbed two-point boundary value problems with a boundary layer at one end point. The two-point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a seventh order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two-point boundary value problem is obtained from the theory of singular perturbations. It is used in the seventh order compact difference scheme to get a two term recurrence relation and is solved. Several linear and nonlinear singular perturbation problems have been solved and the numerical results are presented to support the theory. (C) 2006 Elsevier Inc. All rights reserved.

Keyword:

singular perturbation problems

two-point boundary value problems

ordinary differential equations

boundary layer

seventh order compact difference scheme