scipy.integrate.OdeSolver¶

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:
A constructor must accept parameters presented in the base class (listed below) along with any other parameters specific to a solver.
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.A solver must implement a private method _step_impl(self) which propagates a solver one step further. It must return tuple
(success, message)
, wheresuccess
is a boolean indicating whether a step was successful, andmessage
is a string containing description of a failure if a step failed or None otherwise.A solver must implement a private method _dense_output_impl(self), which returns a
DenseOutput
object covering the last successful step.A solver must have attributes listed below in Attributes section. Note that
t_old
andstep_size
are updated automatically.Use fun(self, t, y) method for the system rhs evaluation, this way the number of function evaluations (nfev) will be tracked automatically.
For convenience, a base class provides fun_single(self, t, y) and fun_vectorized(self, t, y) for evaluating the rhs in nonvectorized and vectorized fashions respectively (regardless of how fun from the constructor is implemented). These calls don’t increment nfev.
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).
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.
 Parameters
 funcallable
Righthand side of the system. The calling signature is
fun(t, y)
. Heret
is a scalar and there are two options for ndarrayy
. It can either have shape (n,), thenfun
must return array_like with shape (n,). Or, alternatively, it can have shape (n, n_points), thenfun
must return array_like with shape (n, n_points) (each column corresponds to a single column iny
). 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.
 vectorizedbool
Whether fun is implemented in a vectorized fashion.
 support_complexbool, optional
Whether integration in a complex domain should be supported. Generally determined by a derived solver class capabilities. 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 of the system’s rhs evaluations.
 njevint
Number of the Jacobian evaluations.
 nluint
Number of LU decompositions.
Methods
Compute a local interpolant over the last successful step.
step
()Perform one integration step.