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 of the system's rhs evaluations.

njev : int

Number of the Jacobian evaluations.

nlu : int

Number of LU decompositions.

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 :None:None:`_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 :None:None:`_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 :None:None:`fun(self, t, y)` method for the system rhs evaluation, this way the number of function evaluations (:None:None:`nfev`) will be tracked automatically.

7. For convenience, a base class provides :None:None:`fun_single(self, t, y)` and :None:None:`fun_vectorized(self, t, y)` for evaluating the rhs in non-vectorized and vectorized fashions respectively (regardless of how :None:None:`fun` from the constructor is implemented). These calls don't increment :None:None:`nfev`.

8. If a solver uses a Jacobian matrix and LU decompositions, it should track the number of Jacobian evaluations (:None:None:`njev`) and the number of LU decompositions (:None:None:`nlu`).

9. By convention, the function evaluations used to compute a finite difference approximation of the Jacobian should not be counted in :None:None:`nfev`, thus use :None:None:`fun_single(self, t, y)` or :None:None:`fun_vectorized(self, t, y)` when computing a finite difference approximation of the Jacobian.

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 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 :None:None:`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 :None:None:`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.

Base class for ODE solvers.

Examples

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.integrate._ivp.ivp.solve_ivp

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