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()