Bulirsch–Stoer algorithm (original) (raw)
In numerical analysis, the Bulirsch–Stoer algorithm is a method for the numerical solution of ordinary differential equations which combines three powerful ideas: Richardson extrapolation, the use of in Richardson-type applications, and the modified midpoint method, to obtain numerical solutions to ordinary differential equations (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.
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| dbo:abstract | In numerical analysis, the Bulirsch–Stoer algorithm is a method for the numerical solution of ordinary differential equations which combines three powerful ideas: Richardson extrapolation, the use of in Richardson-type applications, and the modified midpoint method, to obtain numerical solutions to ordinary differential equations (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. (en) Алгоритм Булирша-Штёра — численный метод решения обыкновенных дифференциальных уравнений, опирающийся на (Richardson extrapolation), на экстраполяцию рациональными функциями (rational function extrapolation) в приложениях Ричардсоновского типа и на (modified midpoint method). Позволяет находить численные решения обыкновенных дифференциальных уравнений с высокой точностью при достаточно малых вычислительных усилиях. Назван в честь (Roland Bulirsch) и (Josef Stoer). Иногда метод называют алгоритмом Грэгга-Булирша-Штёра (Gragg-Bulirsch-Stoer (GBS) algorithm), так как важный результат относительно функции ошибки модифицированного метода средней точки принадлежит Уильяму Б. Грэггу (William B. Gragg). (ru) |
| dbo:wikiPageExternalLink | http://apps.nrbook.com/empanel/index.html%23pg=921 http://www.unige.ch/~hairer/prog/nonstiff/odex.f http://www.unige.ch/~hairer/software.html https://commons.apache.org/proper/commons-math/javadocs/api-3.6.1/org/apache/commons/math3/ode/nonstiff/GraggBulirschStoerIntegrator.html https://www.boost.org/doc/libs/1_55_0/boost/numeric/odeint/stepper/bulirsch_stoer.hpp |
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| rdfs:comment | In numerical analysis, the Bulirsch–Stoer algorithm is a method for the numerical solution of ordinary differential equations which combines three powerful ideas: Richardson extrapolation, the use of in Richardson-type applications, and the modified midpoint method, to obtain numerical solutions to ordinary differential equations (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. (en) Алгоритм Булирша-Штёра — численный метод решения обыкновенных дифференциальных уравнений, опирающийся на (Richardson extrapolation), на экстраполяцию рациональными функциями (rational function extrapolation) в приложениях Ричардсоновского типа и на (modified midpoint method). Позволяет находить численные решения обыкновенных дифференциальных уравнений с высокой точностью при достаточно малых вычислительных усилиях. Назван в честь (Roland Bulirsch) и (Josef Stoer). (ru) |
| rdfs:label | Bulirsch–Stoer algorithm (en) Алгоритм Булирша-Штёра (ru) |
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