def solver_scaled(beta, T, dt, theta=0.5):
"""
Solve u'=-u+1, u(0)=beta for (0,T]
with step dt and theta method.
"""
print 'Computing the numerical solution'
return solver_unscaled(
I=beta, a=lambda t: 1, b=lambda t: 1,
T=T, dt=dt, theta=theta)
def solver_scaled(gamma, T, dt, theta=0.5):
"""
Solve u'=-a*u, u(0)=1 for (0,T] with step dt and theta method.
a=1 for t < gamma and 2 for t > gamma.
"""
print 'Computing the numerical solution'
return solver_unscaled(
I=1, a=lambda t: 1 if t < gamma else 5,
b=lambda t: 0, T=T, dt=dt, theta=theta)
def solver_scaled(alpha, beta, t_stop, dt, theta=0.5):
"""
Solve T' = -T + 1 + alha*sin(beta*t), T(0)=0
for (0,T] with step dt and theta method.
"""
print 'Computing the numerical solution'
return solver_unscaled(
I=0, a=lambda t: 1,
b=lambda t: 1 + alpha*np.sin(beta*t),
T=t_stop, dt=dt, theta=theta)
def solver_scaled(beta, T, dt, theta=0.5):
"""
Solve u'=-u+1, u(0)=beta for (0,T]
with step dt and theta method.
"""
print 'Computing the numerical solution'
return solver_unscaled(I=beta,
a=lambda t: 1,
b=lambda t: 1,
T=T,
dt=dt,
theta=theta)
