def demo():
"""
Demonstrate difference between Euler-Cromer and the
scheme for the corresponding 2nd-order ODE.
"""
I = 1.2
w = 2.0
T = 5
dt = 2 / w # longest possible time step
from vib_undamped import solver as solver2 # 2nd-order ODE
import scitools.std as plt
for k in range(4):
dt /= 4
u2, t2 = solver2(I, w, dt, T)
u, v, t = solver(I, w, dt, T)
plt.figure()
plt.plot(t,
u,
t2,
u2,
legend=('Euler-Cromer', 'center scheme for $u'
'+u=0$'),
title='dt=%.3g' % dt)
raw_input()
plt.savefig('ECvs2nd_%d' % k + '.png')
plt.savefig('ECvs2nd_%d' % k + '.pdf')
def test_staggered():
I = 1.2; w = 2.0; T = 5; dt = 2/w
u, t, v, t_v = solver(I, w, dt, T)
from vib_undamped import solver as solver2
u2, t2 = solver2(I, w, dt, T)
error = abs(u - u2).max()
nt.assert_almost_equal(error, 0, places=14)
def test_staggered():
I = 1.2; w = 2.0; T = 5; dt = 2/w
u, t, v, t_v = solver(I, w, dt, T)
from vib_undamped import solver as solver2
u2, t2 = solver2(I, w, dt, T)
error = abs(u - u2).max()
tol = 1E-14
assert error < tol
def test_staggered():
I = 1.2; w = 2.0; T = 5; dt = 2/w
u, t, v, t_v = solver(I, w, dt, T)
from vib_undamped import solver as solver2
u2, t2 = solver2(I, w, dt, T)
error = abs(u - u2).max()
tol = 1E-14
assert error < tol
def test_solver():
"""
Test solver with fixed ic against equivalent scheme for
the 2nd-order ODE u'' + u = 0.
"""
I = 1.2; w = 2.0; T = 5
dt = 2/w # longest possible time step
u, v, t = solver_ic_fix(I, w, dt, T)
from vib_undamped import solver as solver2 # 2nd-order ODE
u2, t2 = solver2(I, w, dt, T)
error = abs(u - u2).max()
nt.assert_almost_equal(error, 0, places=14)
def test_solver():
"""
Test solver with fixed ic against equivalent scheme for
the 2nd-order ODE u'' + u = 0.
"""
I = 1.2; w = 2.0; T = 5
dt = 2/w # longest possible time step
u, v, t = solver_ic_fix(I, w, dt, T)
from vib_undamped import solver as solver2 # 2nd-order ODE
u2, t2 = solver2(I, w, dt, T)
error = np.abs(u - u2).max()
tol = 1E-14
assert error < tol
def test_solver():
"""
Test solver with fixed initial condition against
equivalent scheme for the 2nd-order ODE u'' + u = 0.
"""
I = 1.2; w = 2.0; T = 5
dt = 2/w # longest possible time step
u, v, t = solver_ic_fix(I, w, dt, T)
from vib_undamped import solver as solver2 # 2nd-order ODE
u2, t2 = solver2(I, w, dt, T)
error = np.abs(u - u2).max()
tol = 1E-14
assert error < tol
def test_solver():
"""
Test solver with fixed ic against equivalent scheme for
the 2nd-order ODE u'' + u = 0.
"""
I = 1.2
w = 2.0
T = 5
dt = 2 / w # longest possible time step
u, v, t = solver_ic_fix(I, w, dt, T)
from vib_undamped import solver as solver2 # 2nd-order ODE
u2, t2 = solver2(I, w, dt, T)
error = abs(u - u2).max()
nt.assert_almost_equal(error, 0, places=14)
def demo():
"""
Demonstrate difference between Euler-Cromer and the
scheme for the corresponding 2nd-order ODE.
"""
I = 1.2; w = 2.0; T = 5
dt = 2/w # longest possible time step
from vib_undamped import solver as solver2 # 2nd-order ODE
from scitools.std import plot, figure, savefig
for k in range(4):
dt /= 4
u2, t2 = solver2(I, w, dt, T)
u, v, t = solver(I, w, dt, T)
figure()
plot(t, u, t2, u2,
legend=('Euler-Cromer', 'center scheme for $u''+u=0$'),
title='dt=%.3g' % dt)
raw_input()
savefig('ECvs2nd_%d' % k + '.png')
savefig('ECvs2nd_%d' % k + '.pdf')
def demo():
"""
Demonstrate difference between Euler-Cromer and the
scheme for the corresponding 2nd-order ODE.
"""
I = 1.2
w = 2.0
T = 5
dt = 2 / w # longest possible time step
from vib_undamped import solver as solver2 # 2nd-order ODE
import scitools.std as plt
for k in range(4):
dt /= 4
u2, t2 = solver2(I, w, dt, T)
u, v, t = solver(I, w, dt, T)
plt.figure()
plt.plot(t, u, t2, u2, legend=("Euler-Cromer", "center scheme for $u" "+u=0$"), title="dt=%.3g" % dt)
raw_input()
plt.savefig("ECvs2nd_%d" % k + ".png")
plt.savefig("ECvs2nd_%d" % k + ".pdf")
