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Module « scipy.integrate »

Classe « RK23 »

Informations générales

Héritage

builtins.object
    OdeSolver
        RungeKutta
            RK23

Définition

class RK23(RungeKutta):

help(RK23)

Explicit Runge-Kutta method of order 3(2).

This uses the Bogacki-Shampine pair of formulas [1]_. The error is controlled
assuming accuracy of the second-order method, but steps are taken using the
third-order accurate formula (local extrapolation is done). A cubic Hermite
polynomial is used for the dense output.

Can be applied in the complex domain.

Parameters
----------
fun : callable
    Right-hand side of the system: the time derivative of the state ``y``
    at time ``t``. The calling signature is ``fun(t, y)``, where ``t`` is a
    scalar and ``y`` is an ndarray with ``len(y) = len(y0)``. ``fun`` must
    return an array of the same shape as ``y``. See `vectorized` for more
    information.
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` may be called in a vectorized fashion. False (default)
    is recommended for this solver.

    If ``vectorized`` is False, `fun` will always be called with ``y`` of
    shape ``(n,)``, where ``n = len(y0)``.

    If ``vectorized`` is True, `fun` may be called with ``y`` of shape
    ``(n, k)``, where ``k`` is an integer. In this case, `fun` must behave
    such that ``fun(t, y)[:, i] == fun(t, y[:, i])`` (i.e. each column of
    the returned array is the time derivative of the state corresponding
    with a column of ``y``).

    Setting ``vectorized=True`` allows for faster finite difference
    approximation of the Jacobian by methods 'Radau' and 'BDF', but
    will result in slower execution for this solver.

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] P. Bogacki, L.F. Shampine, "A 3(2) Pair of Runge-Kutta Formulas",
       Appl. Math. Lett. Vol. 2, No. 4. pp. 321-325, 1989.

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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