Number of equations.
Current status of the solver: 'running', 'finished' or 'failed'.
Boundary time.
Integration direction: +1 or -1.
Current time.
Current state.
Previous time. None if no steps were made yet.
Size of the last successful step. None if no steps were made yet.
Number evaluations of the system's right-hand side.
Number of evaluations of the Jacobian. Is always 0 for this solver as it does not use the Jacobian.
Number of LU decompositions. Is always 0 for this solver.
This is a Python implementation of "DOP853" algorithm originally written in Fortran , . Note that this is not a literate translation, but the algorithmic core and coefficients are the same.
Can be applied in the complex domain.
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 :None:None:`vectorized`
argument (see below).
Initial time.
Initial state.
Boundary time - the integration won't continue beyond it. It also determines the direction of the integration.
Initial step size. Default is None
which means that the algorithm should choose.
Maximum allowed step size. Default is np.inf, i.e. the step size is not bounded and determined solely by the solver.
Relative and absolute tolerances. The solver keeps the local error estimates less than atol + rtol * abs(y)
. Here :None:None:`rtol`
controls a relative accuracy (number of correct digits), while atol
controls absolute accuracy (number of correct decimal places). To achieve the desired :None:None:`rtol`
, set atol
to be lower than the lowest value that can be expected from rtol * abs(y)
so that :None:None:`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 :None:None:`rtol`
such that rtol * abs(y)
is always lower 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 :None:None:`rtol`
and 1e-6 for atol
.
Whether :None:None:`fun`
is implemented in a vectorized fashion. Default is False.
Explicit Runge-Kutta method of order 8.
Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.
Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)
SVG is more flexible but power hungry; and does not scale well to 50 + nodes.
All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them