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In [[numerical analysis]], the '''Bulirsch-Stoer Algorithm''' is a method of [[numerical integration]] 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]] (ODEs) with high accuracy and comparatively little computational effort. It ist named after [[Roland Bulirsch]] and [[Josef Stoer]]. It is sometimes called '''Gragg-Bulirsch-Stoer Algorithm''' because of the importance of a result about the error function of the modified midpoint method, due to [[William B. Gragg]].
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* William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling. ''[[Numerical Recipes|Numerical Recipes in C]]''. Cambridge University Press, 1988. (See chapter 15.)
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