def run_example(with_plots=True):
r"""
Example for the use of the stability limit detection algorithm
in CVode.
.. math::
\dot y_1 &= y_2 \\
\dot y_2 &= \mu ((1.-y_1^2) y_2-y_1) \\
\dot y_3 &= sin(ty_2)
with :math:`\mu=\frac{1}{5} 10^3`.
on return:
- :dfn:`exp_mod` problem instance
- :dfn:`exp_sim` solver instance
"""
class Extended_Problem(Explicit_Problem):
order = []
def handle_result(self, solver, t, y):
Explicit_Problem.handle_result(self, solver, t, y)
self.order.append(solver.get_last_order())
eps = 5.e-3
my = 1./eps
#Define the rhs
def f(t,y):
yd_0 = y[1]
yd_1 = my*((1.-y[0]**2)*y[1]-y[0])
yd_2 = N.sin(t*y[1])
return N.array([yd_0,yd_1, yd_2])
y0 = [2.0,-0.6, 0.1] #Initial conditions
#Define an Assimulo problem
exp_mod = Extended_Problem(f,y0,
name = "CVode: Stability problem")
#Define an explicit solver
exp_sim = CVode(exp_mod) #Create a CVode solver
#Sets the parameters
exp_sim.stablimdet = True
exp_sim.report_continuously = True
#Simulate
t, y = exp_sim.simulate(2.0) #Simulate 2 seconds
#Plot
if with_plots:
P.subplot(211)
P.plot(t,y[:,2])
P.ylabel("State: $y_1$")
P.subplot(212)
P.plot(t,exp_mod.order)
P.ylabel("Order")
P.suptitle(exp_mod.name)
P.xlabel("Time")
P.show()
#Basic test
x1 = y[:,0]
assert N.abs(x1[-1]-1.8601438) < 1e-1 #For test purpose
return exp_mod, exp_sim
