`scipy.integrate._ivp.rk:rk_step`

Signature

def rk_step(fun, t, y, f, h, A, B, C, K)

Perform a single Runge-Kutta step.

This function computes a prediction of an explicit Runge-Kutta method and also estimates the error of a less accurate method.

Notation for Butcher tableau is as in ^[1].

fun : callable: Right-hand side of the system.
t : float: Current time.
y : ndarray, shape (n,): Current state.
f : ndarray, shape (n,): Current value of the derivative, i.e., fun(x, y).
h : float: Step to use.
A : ndarray, shape (n_stages, n_stages): Coefficients for combining previous RK stages to compute the next stage. For explicit methods the coefficients at and above the main diagonal are zeros.
B : ndarray, shape (n_stages,): Coefficients for combining RK stages for computing the final prediction.
C : ndarray, shape (n_stages,): Coefficients for incrementing time for consecutive RK stages. The value for the first stage is always zero.
K : ndarray, shape (n_stages + 1, n): Storage array for putting RK stages here. Stages are stored in rows. The last row is a linear combination of the previous rows with coefficients

y_new : ndarray, shape (n,): Solution at t + h computed with a higher accuracy.
f_new : ndarray, shape (n,): Derivative fun(t + h, y_new).