class scipy.integrate.OdeSolver(fun, t0, y0, t_bound, vectorized, support_complex=False)[source]

Base class for ODE solvers.

In order to implement a new solver you need to follow the guidelines:

  1. A constructor must accept parameters presented in the base class (listed below) along with any other parameters specific to a solver.
  2. A constructor must accept arbitrary extraneous arguments **extraneous, but warn that these arguments are irrelevant using common.warn_extraneous function. Do not pass these arguments to the base class.
  3. A solver must implement a private method _step_impl(self) which propagates a solver one step further. It must return tuple (success, message), where success is a boolean indicating whether a step was successful, and message is a string containing description of a failure if a step failed or None otherwise.
  4. A solver must implement a private method _dense_output_impl(self) which returns a DenseOutput object covering the last successful step.
  5. A solver must have attributes listed below in Attributes section. Note that t_old and step_size are updated automatically.
  6. Use fun(self, t, y) method for the system rhs evaluation, this way the number of function evaluations (nfev) will be tracked automatically.
  7. For convenience a base class provides fun_single(self, t, y) and fun_vectorized(self, t, y) for evaluating the rhs in non-vectorized and vectorized fashions respectively (regardless of how fun from the constructor is implemented). These calls don’t increment nfev.
  8. If a solver uses a Jacobian matrix and LU decompositions, it should track the number of Jacobian evaluations (njev) and the number of LU decompositions (nlu).
  9. By convention the function evaluations used to compute a finite difference approximation of the Jacobian should not be counted in nfev, thus use fun_single(self, t, y) or fun_vectorized(self, t, y) when computing a finite difference approximation of the Jacobian.
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 ndarray y. It can either have shape (n,), then fun must return array_like with shape (n,). Or alternatively it can have shape (n, n_points), then fun must return array_like with shape (n, n_points) (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.

vectorized : bool

Whether fun is implemented in a vectorized fashion.

support_complex : bool, optional

Whether integration in a complex domain should be supported. Generally determined by a derived solver class capabilities. Default is False.

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 of the system’s rhs evaluations.

njev : int

Number of the Jacobian evaluations.

nlu : int

Number of LU decompositions.


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