`scipy.integrate._ivp.common:select_initial_step`

Signature

def select_initial_step(fun, t0, y0, t_bound, max_step, f0, direction, order, rtol, atol)

Empirically select a good initial step.

The algorithm is described in ^[1].

fun : callable: Right-hand side of the system.
t0 : float: Initial value of the independent variable.
y0 : ndarray, shape (n,): Initial value of the dependent variable.
t_bound : float: End-point of integration interval; used to ensure that t0+step<=tbound and that fun is only evaluated in the interval [t0,tbound]
max_step : float: Maximum allowable step size.
f0 : ndarray, shape (n,): Initial value of the derivative, i.e., fun(t0, y0).
direction : float: Integration direction.
order : float: Error estimator order. It means that the error controlled by the algorithm is proportional to ``step_size ** (order + 1)`.
rtol : float: Desired relative tolerance.
atol : float: Desired absolute tolerance.