Bulirsch–Stoer algorithm: Difference between revisions

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Revision as of 07:30, 21 April 2013

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In [[numerical analysis]], the '''Bulirsch–Stoer algorithm''' is a method for the [[numerical ordinary differential equations|numerical solution of ordinary differential equations]] which combines three powerful ideas: [[Richardson extrapolation]], the use of [[rational function extrapolation]] in Richardson-type applications, and the [[modified midpoint method]], to obtain numerical solutions to [[ordinary differential equation|ordinary differential equations]]s (ODEs) with high accuracy and comparatively little computational effort. It is named after [[Roland Bulirsch]] and [[Josef Stoer]]. It is sometimes called the '''Gragg–Bulirsch–Stoer (GBS) algorithm''' because of the importance of a result about the error function of the modified midpoint method, due to [[William B. Gragg]].

==Underlying ideas==

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* [http://www.unige.ch/~hairer/prog/nonstiff/odex.f ODEX.F], implementation of the Bulirsch–Stoer algorithm by Ernst Hairer and Gerhard Wanner (for other routines and license conditions, see their [http://www.unige.ch/~hairer/software.html Fortran and Matlab Codes] page).

{{DEFAULTSORT:Bulirsch-Stoer algorithm}}

[[Category:Numerical integration (quadrature)]]