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List of Runge-Kutta methods : ウィキペディア英語版
List of Runge–Kutta methods
Runge–Kutta methods are methods for the numerical solution of the ordinary differential equation
:\frac = f(t, y)\,
which take the form
:y_ = y_n + h \sum_^s b_i k_i\,
:k_i = f\left(t_n + c_i h, y_n + h \sum_^ a_ k_j\right).
The methods listed on this page are each defined by its Butcher tableau, which puts the coefficients of the method in a table as follows:
:
\begin
c_1 & a_ & a_& \dots & a_\\
c_2 & a_ & a_& \dots & a_\\
\vdots & \vdots & \vdots& \ddots& \vdots\\
c_s & a_ & a_& \dots & a_ \\
\hline
& b_1 & b_2 & \dots & b_s\\
\end

==Explicit methods==

The explicit methods are those where the matrix () is lower triangular.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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