def f(u, t):
return -a * u
I = 1
a = 2
T = 6
dt = float(sys.argv[1]) if len(sys.argv) >= 2 else 0.75
Nt = int(round(T / dt))
t_mesh = np.linspace(0, Nt * dt, Nt + 1)
solvers = [
odespy.RK2(f),
odespy.RK3(f),
odespy.RK4(f),
# BackwardEuler must use Newton solver to converge
# (Picard is default and leads to divergence)
odespy.BackwardEuler(f, nonlinear_solver='Newton')
]
legends = []
for solver in solvers:
solver.set_initial_condition(I)
u, t = solver.solve(t_mesh)
plt.plot(t, u)
plt.hold('on')
legends.append(solver.__class__.__name__)
k3 = func(z[i, :] + k2 * dt2, t + dt2) # predictor step 3
k4 = func(z[i, :] + k3 * dt, t + dt) # predictor step 4
z[i + 1, :] = z[i, :] + dt / 6.0 * (k1 + 2.0 * k2 + 2.0 * k3 + k4
) # Corrector step
return z
# Main program starts here
from numpy import linspace
T = 10 # end of simulation
N = 20 # no of time steps
time = linspace(0, T, N + 1)
solvers = []
solvers.append(odespy.RK3(f2))
solvers.append(odespy.RK4(f2))
legends = []
z0 = np.zeros(2)
z0[0] = 2.0
for i, solver in enumerate(solvers):
solver.set_initial_condition(z0)
z, t = solver.solve(time)
plot(t, z[:, 1])
legends.append(str(solver))
scheme_list = [euler, heun, rk4_own]
plt.hold('on')
plt.xlabel('Number of periods')
plt.ylabel('Amplitude (absolute value)')
plt.legend(loc='upper left')
plt.savefig(file_name + '.png')
plt.savefig(file_name + '.pdf')
plt.show()
# Define different sets of experiments
solvers_CNB2 = [
odespy.CrankNicolson(f, nonlinear_solver='Newton'),
odespy.Backward2Step(f)
]
solvers_RK34 = [odespy.RK3(f), odespy.RK4(f)]
solvers_AB = [odespy.AdamsBashforth2(f), odespy.AdamsBashforth3(f)]
if __name__ == '__main__':
# Default values
timesteps_per_period = 30
solver_collection = 'CNB2'
num_periods = 100
# Override from command line
try:
# Example: python vib_undamped_odespy.py 30 RK34 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
def fblasius(y, x):
"""ODE-system for the Blasius-equation"""
return [y[1],y[2], -y[0]*y[2]]
import odespy
solvers=[]
solvers.append(odespy.RK4(fblasius))
solvers.append(odespy.RK2(fblasius))
solvers.append(odespy.RK3(fblasius))
from numpy import linspace, exp
xmin = 0
xmax = 5.75
N = 150 # no x-values
xspan = linspace(xmin, xmax, N+1)
smin=0.1
smax=0.8
Ns=30
srange = linspace(smin,smax,Ns)
from matplotlib.pyplot import *
#change some default values to make plots more readable on the screen
LNWDT=5; FNT=25
matplotlib.rcParams['lines.linewidth'] = LNWDT; matplotlib.rcParams['font.size'] = FNT
figure()
legends=[]
linet=['r-',':','.','-.','--']
odespy.AdamsBashforth2(problem),
odespy.AdamsBashforth3(problem),
odespy.AdamsBashforth4(problem),
odespy.AdaptiveResidual(problem, solver='Euler'),
odespy.Backward2Step(problem),
odespy.BackwardEuler(problem),
odespy.Dop853(problem, rtol=rtol, atol=atol),
odespy.Dopri5(problem, rtol=rtol, atol=atol),
odespy.Euler(problem),
odespy.Heun(problem),
odespy.Leapfrog(problem),
odespy.LeapfrogFiltered(problem),
odespy.MidpointImplicit(problem),
odespy.MidpointIter(problem, max_iter=10, eps_iter=1E-7),
odespy.RK2(problem),
odespy.RK3(problem),
odespy.RK4(problem),
odespy.RKFehlberg(problem, rtol=rtol, atol=atol),
odespy.SymPy_odefun(problem),
odespy.ThetaRule(problem),
odespy.Trapezoidal(problem),
odespy.Vode(problem, rtol=rtol, atol=atol, adams_or_bdf=adams_or_bdf),
]
theta_exact = lambda t: problem.Theta * numpy.cos(sqrt(problem.c) * t)
import sys, time
try:
num_periods = int(sys.argv[1])
except IndexError:
num_periods = 30 # default