Journal of applied mathematics & informatics
- Volume 23 Issue 1_2
- /
- Pages.141-152
- /
- 2007
- /
- 2734-1194(pISSN)
- /
- 2234-8417(eISSN)
AN ASYMPTOTIC INITIAL VALUE METHOD FOR SECOND ORDER SINGULAR PERTURBATION PROBLEMS OF CONVECTION-DIFFUSION TYPE WITH A DISCONTINUOUS SOURCE TERM
- Valanarasu, T. (Department of Mathematics, School of Mathematics and Computer Science, Bharathidasan University) ;
- Ramanujam, N. (Department of Mathematics, School of Mathematics and Computer Science, Bharathidasan University)
- Published : 2007.01.31
Abstract
In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.
Keywords
- Singular perturbation problems;
- boundary value problem;
- discontinuous source term;
- boundary and interior layers;
- asymptotic expansion approximation;
- initial value problem;
- initial value method