Source code for assimulo.examples.radau5dae_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 Radau5DAE
from assimulo.problem import Implicit_Problem
[docs]def run_example(with_plots=True):
r"""
Example for the use of Radau5DAE 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:`imp_mod` problem instance
- :dfn:`imp_sim` solver instance
"""
#Define the residual
def f(t,y,yd):
eps = 1.e-6
my = 1./eps
yd_0 = y[1]
yd_1 = my*((1.-y[0]**2)*y[1]-y[0])
res_0 = yd[0]-yd_0
res_1 = yd[1]-yd_1
return N.array([res_0,res_1])
y0 = [2.0,-0.6] #Initial conditions
yd0 = [-.6,-200000.]
#Define an Assimulo problem
imp_mod = Implicit_Problem(f,y0,yd0)
imp_mod.name = 'Van der Pol (implicit)'
#Define an explicit solver
imp_sim = Radau5DAE(imp_mod) #Create a Radau5 solver
#Sets the parameters
imp_sim.atol = 1e-4 #Default 1e-6
imp_sim.rtol = 1e-4 #Default 1e-6
imp_sim.inith = 1.e-4 #Initial step-size
#Simulate
t, y, yd = imp_sim.simulate(2.) #Simulate 2 seconds
#Plot
if with_plots:
P.subplot(211)
P.plot(t,y[:,0])#, marker='o')
P.xlabel('Time')
P.ylabel('State')
P.subplot(212)
P.plot(t,yd[:,0]*1.e-5)#, marker='o')
P.xlabel('Time')
P.ylabel('State derivatives scaled with $10^{-5}$')
P.suptitle(imp_mod.name)
P.show()
#Basic test
x1 = y[:,0]
assert N.abs(x1[-1]-1.706168035) < 1e-3 #For test purpose
return imp_mod, imp_sim
if __name__=='__main__':
mod,sim = run_example()