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

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 .

Parameters

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

Returns

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) .

Perform a single Runge-Kutta step.

Examples

See :

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GitHub : /scipy/integrate/_ivp/rk.py#14
type: <class 'function'>
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