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Radau5DAE

Radau IIA fifth-order three-stages with step-size control and continuous output. Based on the FORTRAN code RADAU5 by E.Hairer and G.Wanner, which can be found here: http://www.unige.ch/~hairer/software.html

Details about the implementation (FORTRAN) can be found in the book,:

Solving Ordinary Differential Equations II,
Stiff and Differential-Algebraic Problems

Authors: E. Hairer and G. Wanner
Springer-Verlag, ISBN: 3-540-60452-9

Support

  • State events (root funtions) : True
  • Step events (completed step) : True
  • Time events : True

Usage

Import the solver together with the correct problem:

from assimulo.solvers import Radau5DAE
from assimulo.problem import Implicit_Problem

Define the problem, such as:

def res(t, y, yd): #Note that y and yd are 1-D numpy arrays.
    res = yd[0]-1.0
    return N.array([res]) #Note that the return must be numpy array, NOT a scalar.

y0  = [1.0]
yd0 = [1.0]
t0  = 1.0

Create a problem instance:

mod = Implicit_Problem(res, y0, yd0, t0)

Note

For complex problems, it is recommended to check the available examples and the documentation in the problem class, Implicit_Problem. It is also recommended to define your problem as a subclass of Implicit_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 = Radau5DAE(mod)

Modify (optionally) the solver parameters.

Parameters:

  • atol Defines the absolute tolerance(s) that is to be used by the solver.
  • 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.
  • fac1 Parameters for step-size selection.
  • fac2 Parameters for step-size selection.
  • fnewt Stopping criterion for Newton’s method, usually chosen <1.
  • inith This determines the initial step-size to be used in the integration.
  • maxh Defines the maximal step-size that is to be used by the solver.
  • maxsteps The maximum number of steps allowed to be taken to reach the final time.
  • newt Maximal number of Newton iterations.
  • num_threads This options specifies the number of threads to be used for those solvers that supports it.
  • quot1 If quot1 < current step-size / old step-size < quot2 the the step-size is not changed.
  • quot2 If quot1 < current step-size / old step-size < quot2 the the step-size is not changed.
  • report_continuously This options specifies if the solver should report the solution continuously after steps.
  • rtol Defines the relative tolerance that is to be used by the solver.
  • safe The safety factor in the step-size prediction.
  • store_event_points This options specifies if the solver should save additional points at the events, \(t_e^-, t_e^+\).
  • thet Value for determine if the Jacobian is to be recomputed or not.
  • time_limit This option can be used to limit the time of an integration.
  • usejac This sets the option to use the user defined jacobian.
  • verbosity This determines the level of the output.

Methods:

  • Radau5DAE.interpolate

Simulate the problem:

Information:

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