Bogacki–Shampine method (Q4937332)

embedded Runge–Kutta method for numerically solving differential equations

Language	Label	Description	Also known as
English	Bogacki–Shampine method	embedded Runge–Kutta method for numerically solving differential equations

Statements

instance of

embedded Runge-Kutta method

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named after

Przemyslaw Bogacki

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Lawrence Fred Shampine

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time of discovery or invention

1989

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defining formula

{\begin{aligned}k_{1}&=f(t_{n},y_{n})\\k_{2}&=f\left(t_{n}+{\frac {1}{2}}h_{n},y_{n}+{\frac {1}{2}}h_{n}k_{1}\right)\\k_{3}&=f\left(t_{n}+{\frac {3}{4}}h_{n},y_{n}+{\frac {3}{4}}h_{n}k_{2}\right)\\y_{n+1}&=y_{n}+{\frac {2}{9}}h_{n}k_{1}+{\frac {1}{3}}h_{n}k_{2}+{\frac {4}{9}}h_{n}k_{3}\\k_{4}&=f(t_{n}+h_{n},y_{n+1})\\z_{n+1}&=y_{n}+{\frac {7}{24}}h_{n}k_{1}+{\frac {1}{4}}h_{n}k_{2}+{\frac {1}{3}}h_{n}k_{3}+{\frac {1}{8}}h_{n}k_{4}.\end{aligned}}

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has characteristic

first same as last property

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number of stages

quantity

4

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maintained by WikiProject

WikiProject Mathematics

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Butcher tableau

{\begin{array}{r|ll}0\\1/2&1/2\\3/4&0&3/4\\1&2/9&1/3&4/9\\\hline &2/9&1/3&4/9&0\\&7/24&1/4&1/3&1/8\end{array}}

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Identifiers

Freebase ID

/m/04mybdd

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Microsoft Academic ID

42099017

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Bogacki–Shampine method (Q4937332)

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Bogacki–Shampine method (Q4937332)

Statements

Identifiers

Sitelinks

Wikipedia(3 entries)

Wikibooks(0 entries)

Wikinews(0 entries)

Wikiquote(0 entries)

Wikisource(0 entries)

Wikiversity(0 entries)

Wikivoyage(0 entries)

Wiktionary(0 entries)

Multilingual sites(0 entries)

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