def run_example(with_plots=True):
r"""
Demonstration of the use of the use of the explicit euler method by solving the
linear test equation :math:`\dot y = - y`
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
#Defines the rhs
def f(t, y):
ydot = -y[0]
return N.array([ydot])
#Define an Assimulo problem
exp_mod = Explicit_Problem(f,
4.0,
name='ExplicitEuler Example: $\dot y = - y$')
#Explicit Euler
exp_sim = ExplicitEuler(exp_mod) #Create a explicit Euler solver
exp_sim.options["continuous_output"] = True
#Simulate
t1, y1 = exp_sim.simulate(3) #Simulate 3 seconds
t2, y2 = exp_sim.simulate(5, 100) #Simulate 2 second more
#Plot
if with_plots:
import pylab as P
P.plot(t1, y1, color="b")
P.plot(t2, y2, color="r")
P.title(exp_mod.name)
P.ylabel('y')
P.xlabel('Time')
P.show()
#Basic test
nose.tools.assert_almost_equal(float(y2[-1]), 0.02628193)
return exp_mod, exp_sim
def run_example(with_plots=True):
r"""
Example of the use of Euler's method for a differential equation
with a discontinuity (state event) and the need for an event iteration.
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
exp_mod = Extended_Problem() #Create the problem
exp_sim = ExplicitEuler(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
#Plot
if with_plots:
import pylab as P
P.plot(t, y)
P.title("Solution of a differential equation with discontinuities")
P.ylabel('States')
P.xlabel('Time')
P.show()
#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)
return exp_mod, exp_sim
def _default_solver_instance(self):
from assimulo.solvers import ExplicitEuler
return ExplicitEuler(self._assimulo_problem)