A Numerical Solution of the Semi Linear Singularly Perturbed Boundary Value Problem Using Multi Region Finite Difference Method

Author

Edwards, David, Jr.

Author_Institution

IJL Res. Center, Newark, VT, USA

fYear

2009

fDate

26-29 Sept. 2009

Firstpage

130

Lastpage

136

Abstract

A multi region finite difference method is described and applied to the one dimension, semi linear, singularly perturbed boundary value problem (SPBVP). The process of developing high precision algorithms for this problem is described and it is shown that when the multi region method is combined with the use of these high order algorithms, numerical solutions can achieve accuracies in the range of 10-20. This represents a gain of between 9 to 14 orders of magnitude over current techniques.

Keywords

boundary-value problems; finite difference methods; numerical analysis; singularly perturbed systems; multi region finite difference method; numerical solutions; semilinear singularly perturbed boundary value problem; Boundary conditions; Boundary value problems; Differential equations; Finite difference methods; Fluid flow; Geometry; Mathematical model; Physics; Scientific computing; Testing; FDM; High Precision; Multi Region FDM; SPBVP; Semi Linear;

fLanguage

English

Publisher

ieee

Conference_Titel

Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2009 11th International Symposium on

Conference_Location

Timisoara

Print_ISBN

978-1-4244-5910-0

Electronic_ISBN

978-1-4244-5911-7

Type

conf

DOI

10.1109/SYNASC.2009.35

Filename

5460857