# scipy.integrate.DOP853

class scipy.integrate.DOP853(fun, t0, y0, t_bound, max_step=inf, rtol=0.001, atol=1e-06, vectorized=False, first_step=None, **extraneous)

  Explicit Runge-Kutta method of order 8.

  This is a Python implementation of “DOP853” algorithm originally written in Fortran [1], [2]. Note that this is not a literate translation, but the algorithmic core and coefficients are the same.

  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). But if a component of y is approximately below atol, the error only needs to fall within the same atol threshold, and the number of correct digits is not guaranteed. 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.

  References

  1

    E. Hairer, S. P. Norsett G. Wanner, “Solving Ordinary Differential Equations I: Nonstiff Problems”, Sec. II.

  2

    Page with original Fortran code of DOP853.

  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.

  Methods

  `dense_output`() | Compute a local interpolant over the last successful step.
  `step`() | Perform one integration step.

scipy.integrate.RK45.step scipy.integrate.DOP853.dense_output