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Module « scipy.integrate »

Classe « RK45 »

Informations générales

Héritage

builtins.object
    OdeSolver
        RungeKutta
            RK45

Définition

class RK45(RungeKutta):

help(RK45)

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

This uses the Dormand-Prince pair of formulas [1]_. 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 [2]_.

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 `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 `rtol` controls a
    relative accuracy (number of correct digits), while `atol` controls
    absolute accuracy (number of correct decimal places). To achieve the
    desired `rtol`, set `atol` to be smaller than the smallest value that
    can be expected from ``rtol * abs(y)`` so that `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 `rtol` such that ``rtol * abs(y)`` is always smaller
    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 `rtol` and 1e-6 for `atol`.
vectorized : bool, optional
    Whether `fun` is implemented in a vectorized fashion. Default is False.

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.

References
----------
.. [1] J. R. Dormand, P. J. Prince, "A family of embedded Runge-Kutta
       formulae", Journal of Computational and Applied Mathematics, Vol. 6,
       No. 1, pp. 19-26, 1980.
.. [2] L. W. Shampine, "Some Practical Runge-Kutta Formulas", Mathematics
       of Computation,, Vol. 46, No. 173, pp. 135-150, 1986.

Constructeur(s)

Signature du constructeur	Description
__init__(self, fun, t0, y0, t_bound, max_step=inf, rtol=0.001, atol=1e-06, vectorized=False, first_step=None, **extraneous)

Liste des opérateurs

Opérateurs hérités de la classe object

__eq__, __ge__, __gt__, __le__, __lt__, __ne__

Méthodes héritées de la classe RungeKutta

__init_subclass__, __subclasshook__

Méthodes héritées de la classe OdeSolver

dense_output, step

Méthodes héritées de la classe object

__delattr__, __dir__, __format__, __getattribute__, __getstate__, __hash__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__

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