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June 2006 Numerical Green's Function Method Based on the DE Transformation
Masatake Mori, Toshihiko Echigo
Japan J. Indust. Appl. Math. 23(2): 193-205 (June 2006).


A method for numerical solution of boundary value problems with ordinary differential equation based on the method of Green's function incorporated with the double exponential transformation is presented. The method proposed does not require solving a system of linear equations and gives an approximate solution of very high accuracy with a small number of function evaluations. The error of the method is $O\left(\exp\left(-C_1N/\log(C_2N)\right)\right)$ where $N$ is a parameter representing the number of function evaluations and $C_1$ and $C_2$ are some positive constants. Numerical examples also prove the high efficiency of the method. An alternative method via an integral equation is presented which can be used when the Green's function corresponding to the given equation is not available.


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Masatake Mori. Toshihiko Echigo. "Numerical Green's Function Method Based on the DE Transformation." Japan J. Indust. Appl. Math. 23 (2) 193 - 205, June 2006.


Published: June 2006
First available in Project Euclid: 12 September 2006

zbMATH: 1104.65076
MathSciNet: MR2245700

Keywords: boundary value problem , DE transformation , double exponential transformation , Green's function , integral equation

Rights: Copyright © 2006 The Japan Society for Industrial and Applied Mathematics

Vol.23 • No. 2 • June 2006
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