Skip to main content
`Ctrl`+`K`
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 literal translation, but the algorithmic core and coefficients are the same.

  Can be applied in the complex domain.

  Parameters:
    funcallable

      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).

    t0float

      Initial time.

    y0array_like, shape (n,)

      Initial state.

    t_boundfloat

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

    first_stepfloat or None, optional

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

    max_stepfloat, optional

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

    rtol, atolfloat 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.

    vectorizedbool, optional

      Whether fun is implemented in a vectorized fashion. Default is False.

  Attributes:
    nint

      Number of equations.

    statusstring

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

    t_boundfloat

      Boundary time.

    directionfloat

      Integration direction: +1 or -1.

    tfloat

      Current time.

    yndarray

      Current state.

    t_oldfloat

      Previous time. None if no steps were made yet.

    step_sizefloat

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

    nfevint

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

    njevint

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

    nluint

      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.

  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.