Adaptive Runge-Kutta of order four.
Obs. Step rejection not implemented.
Import the solver together with the correct problem:
from assimulo.solvers import RungeKutta34
from assimulo.problem import Explicit_Problem
Define the problem, such as:
def rhs(t, y): #Note that y are a 1-D numpy array.
yd = -1.0
return N.array([yd]) #Note that the return must be numpy array, NOT a scalar.
y0 = [1.0]
t0 = 1.0
Create a problem instance:
mod = Explicit_Problem(rhs, y0, t0)
Note
For complex problems, it is recommended to check the available examples and the documentation in the problem class, Explicit_Problem
. It is also recommended to define your problem as a subclass of Explicit_Problem
.
Warning
When subclassing from a problem class, the function for calculating the right-hand-side (for ODEs) must be named rhs and in the case with a residual function (for DAEs) it must be named res.
Create a solver instance:
sim = RungeKutta34(mod)
Modify (optionally) the solver parameters.
Parameters:
atol
Sets the absolute tolerance to be used in the integration.backward
Specifies if the simulation is done in reverse time.clock_step
Specifies if the elapsed time of an integrator step should be timed or not.display_progress
This option actives output during the integration in terms of that the current integration is periodically printed to the stdout.inith
This determines the initial step-size to be used in the integration.maxsteps
The maximum number of steps allowed to be taken to reach the final time.num_threads
This options specifies the number of threads to be used for those solvers that supports it.report_continuously
This options specifies if the solver should report the solution continuously after steps.rtol
The relative tolerance to be used in the integration.store_event_points
This options specifies if the solver should save additional points at the events, \(t_e^-, t_e^+\).time_limit
This option can be used to limit the time of an integration.verbosity
This determines the level of the output.
Methods:
RungeKutta34.interpolate
Simulate the problem:
Information:
RungeKutta34.get_options()
Returns the current solver options.RungeKutta34.get_supports()
Returns the functionality which the solver supports.RungeKutta34.get_statistics()
Returns the run-time statistics (if any).RungeKutta34.get_event_data()
Returns the event information (if any).RungeKutta34.print_event_data()
Prints the event information (if any).RungeKutta34.print_statistics()
Prints the run-time statistics for the problem.