(Q4937332)

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Bogacki–Shampine method

embedded Runge–Kutta method for numerically solving differential equations

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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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(Q4937332)

Bogacki–Shampine method

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