Bulirsch–Stoer algorithm: Difference between revisions

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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,<ref>http://www.xmds.org/bulirschStoer.html</ref>, to obtain numerical solutions to [[ordinary differential equation]]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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==References==

{{Reflist}}

* {{Citation | last1=Deuflhard | first1=Peter | title=Order and stepsize control in extrapolation methods | doi=10.1007/BF01418332 | year=1983 | journal=Numerische Mathematik | issn=0029-599X | volume=41 | issue=3 | pages=399–422}}.

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==External links==

* [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).

* [https://www.boost.org/doc/libs/1_55_0/boost/numeric/odeint/stepper/bulirsch_stoer.hpp BOOST library], implementation in C++.

* [https://commons.apache.org/proper/commons-math/javadocs/api-3.6.1/org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html Apache Commons Math], implementation in Java.