solprop.stepper.runge_kutta#

The interaction-picture Runge-Kutta march as a run’s integrator.

A run is stepped by one of two integrators: RungeKutta, the embedded explicit Runge-Kutta pair in the interaction picture (IP-DOPRI5 by default), or solprop.stepper.multistep.Multistep, the low-call Adams method, which is the default. docs/guide/numerics/choosing-a-stepper.md compares them.

Classes

RungeKutta([tableau])

The interaction-picture Runge-Kutta march with an embedded error estimate.

class solprop.stepper.runge_kutta.RungeKutta(tableau=Tableau(name='DOPRI5', nodes=array([0., 0.2, 0.3, 0.8, 0.88888889, 1., 1.]), matrix=array([[0., 0., 0., 0., 0., 0., 0.], [0.2, 0., 0., 0., 0., 0., 0.], [0.075, 0.225, 0., 0., 0., 0., 0.], [0.97777778, -3.73333333, 3.55555556, 0., 0., 0., 0.], [2.95259869, -11.59579332, 9.82289285, -0.29080933, 0., 0., 0.], [2.84627525, -10.75757576, 8.90642272, 0.27840909, -0.2735313, 0., 0.], [0.09114583, 0., 0.4492363, 0.65104167, -0.32237618, 0.13095238, 0.]]), solution_weights=array([0.09114583, 0., 0.4492363, 0.65104167, -0.32237618, 0.13095238, 0.]), error_weights=array([0.00123264, 0., -0.00425277, 0.03697917, -0.0508638, 0.04190476, -0.025]), order=5, embedded_order=4, first_same_as_last=True))[source]#

Bases: object

The interaction-picture Runge-Kutta march with an embedded error estimate.

Every accepted step pays the tableau’s stages in source calls (six for DOPRI5, the first-same-as-last stage recycled) and keeps no history, where the Adams method holds from seven to about sixty further copies of the state, by backend and formulation: the integrator to choose when a source evaluation is cheap or the state is too large for the Adams history (docs/guide/numerics/choosing-a-stepper.md).

Equality is by the tableau’s identity, as Tableau compares.

Attributes:

tableausolprop.stepper.tableau.Tableau: The scheme. Default DOPRI5, whose continuous extension interpolates save planes.

Examples

>>> from solprop.stepper.runge_kutta import RungeKutta
>>> from solprop.stepper.tableau import TSIT5
>>> RungeKutta()
RungeKutta(tableau=DOPRI5)
>>> RungeKutta(TSIT5).name
'Tsit5'

property name: str[source]#

Return the tableau’s name, the method’s record name.

Returns:

str: The tableau’s name.

tableau: Tableau = Tableau(name='DOPRI5', nodes=array([0. , 0.2 , 0.3 , 0.8 , 0.88888889, 1. , 1. ]), matrix=array([[ 0. , 0. , 0. , 0. , 0. , 0. , 0. ], [ 0.2 , 0. , 0. , 0. , 0. , 0. , 0. ], [ 0.075 , 0.225 , 0. , 0. , 0. , 0. , 0. ], [ 0.97777778, -3.73333333, 3.55555556, 0. , 0. , 0. , 0. ], [ 2.95259869, -11.59579332, 9.82289285, -0.29080933, 0. , 0. , 0. ], [ 2.84627525, -10.75757576, 8.90642272, 0.27840909, -0.2735313 , 0. , 0. ], [ 0.09114583, 0. , 0.4492363 , 0.65104167, -0.32237618, 0.13095238, 0. ]]), solution_weights=array([ 0.09114583, 0. , 0.4492363 , 0.65104167, -0.32237618, 0.13095238, 0. ]), error_weights=array([ 0.00123264, 0. , -0.00425277, 0.03697917, -0.0508638 , 0.04190476, -0.025 ]), order=5, embedded_order=4, first_same_as_last=True)#