def convergence_rate():
"""What is the convergence rate of the Euler-Cromer method?"""
from vib_undamped import convergence_rates
def solver_wrapper(I, w, dt, T):
# convergence_rates demands a solver that returns u, t
u, v, t = solver(I, w, dt, T)
return u, t
def solver_ic_fix_wrapper(I, w, dt, T):
# convergence_rates demands a solver that returns u, t
u, v, t = solver(I, w, dt, T)
return u, t
def solver_adjust_w_wrapper(I, w, dt, T):
# convergence_rates demands a solver that returns u, t
u, v, t = solver_adjust_w(I, w, dt, T, True)
return u, t
# Plain Euler-Cromer
r = convergence_rates(8, solver_wrapper)
print(round(r[-1], 1))
# Does it help to fix the initia condition?
r = convergence_rates(8, solver_ic_fix_wrapper)
print(round(r[-1], 1))
# Adjusted w
r = convergence_rates(8, solver_adjust_w_wrapper)
print(round(r[-1], 1))
def convergence_rate():
"""What is the convergence rate of the Euler-Cromer method?"""
from vib_undamped import convergence_rates
def solver_wrapper(I, w, dt, T):
# convergence_rates demands a solver that returns u, t
u, v, t = solver(I, w, dt, T)
return u, t
def solver_ic_fix_wrapper(I, w, dt, T):
# convergence_rates demands a solver that returns u, t
u, v, t = solver(I, w, dt, T)
return u, t
def solver_adjust_w_wrapper(I, w, dt, T):
# convergence_rates demands a solver that returns u, t
u, v, t = solver_adjust_w(I, w, dt, T, True)
return u, t
# Plain Euler-Cromer
r = convergence_rates(8, solver_wrapper)
print round(r[-1], 1)
# Does it help to fix the initia condition?
r = convergence_rates(8, solver_ic_fix_wrapper)
print round(r[-1], 1)
# Adjusted w
r = convergence_rates(8, solver_adjust_w_wrapper)
print round(r[-1], 1)
def test_convergence():
"""Verify 2nd-order convergence."""
from vib_undamped import convergence_rates
def wrapped_solver(I, w, dt, T):
u, t, v, t_v = solver(I, w, dt, T)
return u, t
r = convergence_rates(8, wrapped_solver, 8)
print r
assert abs(r[-1] - 2) < 1E-5
def test_convergence():
"""Verify 2nd-order convergence."""
from vib_undamped import convergence_rates
def wrapped_solver(I, w, dt, T):
u, t, v, t_v = solver(I, w, dt, T)
return u, t
r = convergence_rates(8, wrapped_solver, 8)
print r
assert abs(r[-1] - 2) < 1E-5
from vib_undamped import (zeros, linspace, convergence_rates, main)
def solver(I, w, dt, T, return_v=False):
"""
Solve u'=v, v'=-w**2*u for t in (0,T], u(0)=I and v(0)=0,
by the velocity Verlet method with time step dt.
"""
dt = float(dt)
Nt = int(round(T / dt))
u = zeros(Nt + 1)
v = zeros(Nt + 1)
t = linspace(0, Nt * dt, Nt + 1)
u[0] = I
v[0] = 0
for n in range(Nt):
u[n + 1] = u[n] + v[n] * dt - 0.5 * dt**2 * w**2 * u[n]
v[n + 1] = v[n] - 0.5 * dt * w**2 * (u[n] + u[n + 1])
if return_v:
return u, v, t
else:
# Return just u and t as in the vib_undamped.py's solver
return u, t
if __name__ == '__main__':
main(solver_function=solver)
raw_input()
print convergence_rates(m=5, solver_function=solver)
zeros, linspace,
convergence_rates,
main)
def solver(I, w, dt, T, return_v=False):
"""
Solve u'=v, v'=-w**2*u for t in (0,T], u(0)=I and v(0)=0,
by the velocity Verlet method with time step dt.
"""
dt = float(dt)
Nt = int(round(T/dt))
u = zeros(Nt+1)
v = zeros(Nt+1)
t = linspace(0, Nt*dt, Nt+1)
u[0] = I
v[0] = 0
for n in range(Nt):
u[n+1] = u[n] + v[n]*dt - 0.5*dt**2*w**2*u[n]
v[n+1] = v[n] - 0.5*dt*w**2*(u[n] + u[n+1])
if return_v:
return u, v, t
else:
# Return just u and t as in the vib_undamped.py's solver
return u, t
if __name__ == '__main__':
main(solver_function=solver)
raw_input()
print convergence_rates(m=5, solver_function=solver)
