Bidirectional Shooting: A Strategy to Improve the Reliability of Shooting Methods for ODE

Autor:	Martin Hermann, Pieter P. N. de Groen
Rok vydání:	1984
Předmět:	Singular value Matrix (mathematics) Shooting method Differential equation Ordinary differential equation Singular value decomposition Mathematical analysis Ode Boundary value problem Mathematics
Zdroj:	SIAM Journal on Scientific and Statistical Computing. 5:360-369
ISSN:	2168-3417 0196-5204
DOI:	10.1137/0905027
Popis:	A new shooting technique for the numerical treatment of boundary value problems in ordinary differential equations is proposed. It improves the accuracy and robustness of the simple (unidirectional) shooting method by combining the fundamental matrices originating from both endpoints of the interval. The combination is performed such that the smaller singular values of these matrices and the corresponding orthogonal projections are eliminated. The reason for this strategy is that perturbations of a matrix have a much stronger effect on the smaller singular values than on the larger ones.
Databáze:	OpenAIRE
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