def run_example(with_plots=True):
#Create an instance of the problem
exp_mod = Extended_Problem() #Create the problem
exp_sim = Radau5ODE(exp_mod) #Create the solver
exp_sim.verbosity = 0
exp_sim.report_continuously = True
#Simulate
t, y = exp_sim.simulate(
10.0, 1000) #Simulate 10 seconds with 1000 communications points
#Basic test
nose.tools.assert_almost_equal(y[-1][0], 8.0)
nose.tools.assert_almost_equal(y[-1][1], 3.0)
nose.tools.assert_almost_equal(y[-1][2], 2.0)
#Plot
if with_plots:
P.plot(t, y)
P.title("Solution of a differential equation with discontinuities")
P.ylabel('States')
P.xlabel('Time')
P.show()
return exp_mod, exp_sim
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
#Plot
if with_plots:
import pylab as P
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
def _default_solver_instance(self):
from assimulo.solvers import Radau5ODE
return Radau5ODE(self._assimulo_problem)