Attributes

n : int

Number of equations.

status : string

Current status of the solver: 'running', 'finished' or 'failed'.

t_bound : float

Boundary time.

direction : float

Integration direction: +1 or -1.

t : float

Current time.

y : ndarray

Current state.

t_old : float

Previous time. None if no steps were made yet.

step_size : float

Size of the last successful step. None if no steps were made yet.

nfev : int

Number evaluations of the system's right-hand side.

njev : int

Number of evaluations of the Jacobian. Is always 0 for this solver as it does not use the Jacobian.

nlu : int

Number of LU decompositions. Is always 0 for this solver.

This uses the Dormand-Prince pair of formulas . The error is controlled assuming accuracy of the fourth-order method accuracy, but steps are taken using the fifth-order accurate formula (local extrapolation is done). A quartic interpolation polynomial is used for the dense output .

Can be applied in the complex domain.

Parameters

fun : callable

Right-hand side of the system. The calling signature is fun(t, y) . Here t is a scalar, and there are two options for the ndarray y : It can either have shape (n,); then fun must return array_like with shape (n,). Alternatively it can have shape (n, k); then fun must return an array_like with shape (n, k), i.e., each column corresponds to a single column in y . The choice between the two options is determined by :None:None:`vectorized` argument (see below).

t0 : float

Initial time.

y0 : array_like, shape (n,)

Initial state.

t_bound : float

Boundary time - the integration won't continue beyond it. It also determines the direction of the integration.

first_step : float or None, optional

Initial step size. Default is None which means that the algorithm should choose.

max_step : float, optional

Maximum allowed step size. Default is np.inf, i.e., the step size is not bounded and determined solely by the solver.

rtol, atol : float and array_like, optional

Relative and absolute tolerances. The solver keeps the local error estimates less than atol + rtol * abs(y) . Here :None:None:`rtol` controls a relative accuracy (number of correct digits), while atol controls absolute accuracy (number of correct decimal places). To achieve the desired :None:None:`rtol`, set atol to be lower than the lowest value that can be expected from rtol * abs(y) so that :None:None:`rtol` dominates the allowable error. If atol is larger than rtol * abs(y) the number of correct digits is not guaranteed. Conversely, to achieve the desired atol set :None:None:`rtol` such that rtol * abs(y) is always lower than atol . If components of y have different scales, it might be beneficial to set different atol values for different components by passing array_like with shape (n,) for atol . Default values are 1e-3 for :None:None:`rtol` and 1e-6 for atol .

vectorized : bool, optional

Whether :None:None:`fun` is implemented in a vectorized fashion. Default is False.

Explicit Runge-Kutta method of order 5(4).

Examples

See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

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GitHub : /scipy/integrate/_ivp/rk.py#280
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