Source code for assimulo.examples.radau5ode_vanderpol
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright (C) 2010 Modelon AB
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, version 3 of the License.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
import numpy as N
import pylab as P
import nose
from assimulo.solvers import Radau5ODE
from assimulo.problem import Explicit_Problem
[docs]def run_example(with_plots=True):
r"""
Example for the use of the implicit Euler method to solve
Van der Pol's equation
.. math::
\dot y_1 &= y_2 \\
\dot y_2 &= \mu ((1.-y_1^2) y_2-y_1)
with :math:`\mu= 10^6`.
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
#Define the rhs
def f(t,y):
eps = 1.e-6
my = 1./eps
yd_0 = y[1]
yd_1 = my*((1.-y[0]**2)*y[1]-y[0])
return N.array([yd_0,yd_1])
y0 = [2.0,-0.6] #Initial conditions
#Define an Assimulo problem
exp_mod = Explicit_Problem(f,y0)
exp_mod.name = 'Van der Pol (explicit)'
#Define an explicit solver
exp_sim = Radau5ODE(exp_mod) #Create a Radau5 solver
#Sets the parameters
exp_sim.atol = 1e-4 #Default 1e-6
exp_sim.rtol = 1e-4 #Default 1e-6
exp_sim.inith = 1.e-4 #Initial step-size
#Simulate
t, y = exp_sim.simulate(2.) #Simulate 2 seconds
print(y)
#Plot
if with_plots:
P.plot(t,y[:,0])#, marker='o')
P.xlabel('Time')
P.ylabel('State')
P.title(exp_mod.name)
P.show()
#Basic test
x1 = y[:,0]
assert N.abs(x1[-1]-1.706168035) < 1e-3 #For test purpose
return exp_mod, exp_sim
if __name__=='__main__':
mod,sim = run_example()