def test_newmark_basic_2nd_order_no_damping():
""" Test the explicit case of newmark of simple a 2nd order ODE,
ybis = constant"""
f = lambda t: 9.82/2.0 * t**2 + 5
""" Take off in a rocket at g-acc from 5m above grounds """
f2 = lambda t, x, y: 9.82
y0 = 5.0
v0 = 0.0
prob = Explicit_Problem(f2, y0)
nmark = Newmark(prob, v0)
end = 10.0
t, y = nmark.simulate(end)
print y[-1], f(end), t[-1]
nose.tools.assert_almost_equal(y[-1], f(end))
def test_newmark_basic_2nd_order_damping():
""" Test the implicit case of newmark of simple a 2nd order ODE,
ybis(t) = constant* t. Tests for several values of beta and gamma.
"""
f = lambda t: 5.0/3.0* t**3 + 2*t + 3
""" Take off in a rocket at g-acc from 5m above ground, v0 = 10m/s """
def ode_2(t,x,y):
return 10.0 * t
y0 = 3.0
v0 = 2.0
prob = Explicit_Problem(ode_2, y0)
vals = array([0.0,0.33,0.66,1.0])
for beta in vals:
for gamma in vals:
nmark = Newmark(prob, v0, beta=beta, gamma=gamma)
end = 10.0
t, y = nmark.simulate(end)
nose.tools.assert_almost_equal(y[-1]/y[-1], f(end)/y[-1],places = 1)
def test_pend_newmark_against_normal():
""" Test out newmark solver againts the pendulum by comparing the result
of a simulation against one done by assimulo"""
import problems as p
from matplotlib.pylab import plot, show
pend = p.Pendulum2nd()
ode = pend.fcn
end = 15
y0 = pend.initial_condition()
prob = Explicit_Problem(ode, y0[0])
nmark = Newmark(prob, y0[1], beta = .7, gamma = .5)
t, y_2 = nmark.simulate(end)
ode = pend.fcn_1
prob = Explicit_Problem(ode, y0)
sim = LSODAR(prob)
t, y_3 = sim.simulate(end)
nose.tools.assert_almost_equal(y_3[-1][0]/y_3[-1][0], y_2[-1]/y_3[-1][0],places = 1)