def get_solver(self, func):
"""
Returns the solver method from odespy package.
Args:
func: function
function with ODE system.
Returns: an instance of odeSolver
"""
if self.solverMethod is solverMethod.LSODA:
solver = odespy.Lsoda(func)
elif self.solverMethod is solverMethod.LSODAR:
solver = odespy.Lsodar(func)
elif self.solverMethod is solverMethod.LSODE:
solver = odespy.Lsode(func)
elif self.solverMethod is solverMethod.HEUN:
solver = odespy.Heun(func)
elif self.solverMethod is solverMethod.EULER:
solver = odespy.Euler(func)
elif self.solverMethod is solverMethod.RK4:
solver = odespy.RK4(func)
elif self.solverMethod is solverMethod.DORMAN_PRINCE:
solver = odespy.DormandPrince(func)
elif self.solverMethod is solverMethod.RKFehlberg:
solver = odespy.RKFehlberg(func)
elif self.solverMethod is solverMethod.Dopri5:
solver = odespy.Dopri5(func)
elif self.solverMethod is solverMethod.Dop853:
solver = odespy.Dop853(func)
elif self.solverMethod is solverMethod.Vode:
solver = odespy.Vode(func)
elif self.solverMethod is solverMethod.AdamsBashforth2:
solver = odespy.AdamsBashforth2(func, method='bdf')
elif self.solverMethod is solverMethod.Radau5:
solver = odespy.Radau5(func)
elif self.solverMethod is solverMethod.AdamsBashMoulton2:
solver = odespy.AdamsBashMoulton2(func)
# update default parameters
solver.nsteps = SolverConfigurations.N_STEPS
solver.atol = SolverConfigurations.ABSOLUTE_TOL
solver.rtol = SolverConfigurations.RELATIVE_TOL
return solver
w_F=2 * np.pi) # qualitatively wrong FE, almost ok BE, smaller T
#f = RHS(b=0.4, A_F=20, w_F=0.5*np.pi) # cool, FE almost there, BE good
# Define different sets of experiments
solvers_theta = [
odespy.ForwardEuler(f),
# Implicit methods must use Newton solver to converge
odespy.BackwardEuler(f, nonlinear_solver='Newton'),
odespy.CrankNicolson(f, nonlinear_solver='Newton'),
]
solvers_RK = [odespy.RK2(f), odespy.RK4(f)]
solvers_accurate = [
odespy.RK4(f),
odespy.CrankNicolson(f, nonlinear_solver='Newton'),
odespy.DormandPrince(f, atol=0.001, rtol=0.02)
]
solvers_CN = [odespy.CrankNicolson(f, nonlinear_solver='Newton')]
if __name__ == '__main__':
timesteps_per_period = 20
solver_collection = 'theta'
num_periods = 1
try:
# Example: python vib_odespy.py 30 accurate 50
timesteps_per_period = int(sys.argv[1])
solver_collection = sys.argv[2]
num_periods = int(sys.argv[3])
except IndexError:
pass # default values are ok
solvers = eval('solvers_' + solver_collection) # list of solvers
import scitools.std as plt
def f(u, t):
return -a * u
def exact_solution(t):
return I * np.exp(-a * t)
I = 1
a = 2
T = 5
tol = float(sys.argv[1])
solver = odespy.DormandPrince(f, atol=tol, rtol=0.1 * tol)
N = 1 # just one step - let the scheme find its intermediate points
t_mesh = np.linspace(0, T, N + 1)
t_fine = np.linspace(0, T, 10001)
solver.set_initial_condition(I)
u, t = solver.solve(t_mesh)
# u and t will only consist of [I, u^N] and [0,T]
# solver.u_all and solver.t_all contains all computed points
plt.plot(solver.t_all, solver.u_all, 'ko')
plt.hold('on')
plt.plot(t_fine, exact_solution(t_fine), 'b-')
plt.legend(['tol=%.0E' % tol, 'exact'])
plt.savefig('tmp_odespy_adaptive.png')
