DASP3ODE

DASP3 Solver by Gustaf Söderlind (1980-10-22). Originally published in,:

DASP3 - A Program for the Numerical Integration of Partitioned:
Stiff Ode:s and Differential-Algebraic Systems.

By, Gustaf Söderlind, Department of Numerical Analysis, and
Computing Science, The Royal Institute of Technology, 1980.
Stockholm, Sweden.

DASP3 solves system on the form,

\[\begin{split}\frac{\mathrm{d}y}{\mathrm{d}t} &= f(t,y,z) \;\;\; \text{(N equations)} \\ \varepsilon\frac{\mathrm{d}z}{\mathrm{d}t} &= G(t,y,z)\;\;\; \text{(M equations)}\end{split}\]

If is assumed that the first system is non-stiff and that the stiffness of the second system is due to the parameter epsilon, possibly a diagonal matrix.

Support

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

Usage

Import the solver together with the correct problem:

from assimulo.solvers import DASP3ODE
from assimulo.problem import SingPerturbed_Problem

Define the problem, such as:

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

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

yy0 = [1.0]
zz0 = [1.0]
t0 = 1.0

Create a problem instance:

mod = SingPerturbed_Problem(rhs_slow, rhs_fast, yy0, zz0, t0)

Note

For complex problems, it is recommended to check the available examples and the documentation in the problem class, SingPerturbed_Problem. It is also recommended to define your problem as a subclass of SingPerturbed_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 = DASP3ODE(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.
• 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 Defines the relative tolerance that is to be used by the solver.
• 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.

Simulate the problem:

t, y = DASP3ODE.simulate(tfinal, ncp, ncp_list)

Information:

• DASP3ODE.get_options() Returns the current solver options.
• DASP3ODE.get_supports() Returns the functionality which the solver supports.
• DASP3ODE.get_statistics() Returns the run-time statistics (if any).
• DASP3ODE.get_event_data() Returns the event information (if any).
• DASP3ODE.print_event_data() Prints the event information (if any).
• DASP3ODE.print_statistics() Prints the run-time statistics for the problem.