Classical RK4
The original four-stage, fourth-order method of Kutta
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Stable region in red.
Coefficients
\begin{align} \begin{array}{c|cccc} & & & & \\ \frac{1}{2} & \frac{1}{2} & & & \\ \frac{1}{2} & & \frac{1}{2} & & \\ 1 & & & 1 & \\ \hline & \frac{1}{6} & \frac{1}{3} & \frac{1}{3} & \frac{1}{6} \end{array}\end{align}
Properties
Order of accuracy
: $4$
Stage order
: $1$
Stability function
: $$1 + z + \frac{z^{2}}{2} + \frac{z^{3}}{6} + \frac{z^{4}}{24}$$
Radius of absolute monotonicity
: $0$
Principal error norm: 0.0145045823432
Imaginary stability interval: 2.82842712475
Real stability interval: 2.78529356341
Zero-stable: True