explicit Runge–Kutta method
type of Runge-Kutta method
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explicit Runge–Kutta method
Summary
Key Facts
- explicit Runge–Kutta method's subclass of is recorded as Runge–Kutta method[1].
- explicit Runge–Kutta method's opposite of is recorded as implicit Runge–Kutta method[2].
- explicit Runge–Kutta method's defining formula is recorded as \begin{aligned}k_{1} &=f\left(t_{n}, y_{n}\right) \k_{2} &=f\left(t_{n}+c_{2} h, y_{n}+h\left(a_{21} k_{1}\right)\right) \k_{3} &=f\left(t_{n}+c_{3} h, y_{n}+h\left(a_{31} k_{1}+a_{32} k_{2}\right)\right) \& \vdots \k_{s} &=f\left(t_{n}+c_{s} h, y_{n}+h\left(a_{s 1} k_{1}+a_{s 2} k_{2}+\cdots+a_{s, s-1} k_{s-1}\right)\right) \ y_{n+1}&=y_{n}+h \sum_{i=1}^{s} b_{i} k_{i}\end{aligned}[3].
- explicit Runge–Kutta method's maintained by WikiProject is recorded as WikiProject Mathematics[4].
- explicit Runge–Kutta method's Butcher tableau is recorded as \begin{array}{r|lllll} 0 & & & & & \c_{2} & a_{21} & & & \c_{3} & a_{31} & a_{32} & & \\vdots & \vdots & & \ddots & \c_{s} & a_{s 1} & a_{s 2} & \cdots & a_{s, s-1} \ \hline & b_{1} & b_{2} & \cdots & b_{s-1} & b_{s}\end{array}[5].