Title :
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
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;
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
DOI :
10.1109/SYNASC.2009.35
