def demo_SIR():
"""Test case using an SIR model"""
def f(u, t):
S, I, R = u
return [-beta * S * I, beta * S * I - gamma * I, gamma * I]
beta = 10. / (40 * 8 * 24)
gamma = 3. / (15 * 24)
# 48 h
dt = 48.0
# Simulate for D days
D = 30
# Corresponding no of hours
N_t = int(D * 24 / dt)
# End time
T = dt * N_t
U_0 = [50, 1, 0]
u_old, t_old = ode_FE(f, U_0, dt, T)
S_old = u_old[:, 0]
I_old = u_old[:, 1]
R_old = u_old[:, 2]
k = 1
one_more = True
while one_more == True:
dt_k = 2**(-k) * dt
u_new, t_new = ode_FE(f, U_0, dt_k, T)
S_new = u_new[:, 0]
I_new = u_new[:, 1]
R_new = u_new[:, 2]
plt.plot(t_old, S_old, 'b-', t_new, S_new, 'b--',\
t_old, I_old, 'r-', t_new, I_new, 'r--',\
t_old, R_old, 'g-', t_new, R_new, 'g--')
plt.xlabel('hours')
plt.ylabel('S (blue), I (red), R (green)')
#plt.savefig("SIR_dt_" + str(dt_k) + ".png")
plt.title("dt = " + str(dt_k))
pp.savefig()
plt.clf()
print("Finest timestep was: ", dt_k)
answer = input('Do one more with finer dt (y/n)? ')
if answer == 'y':
S_old = S_new.copy()
R_old = R_new.copy()
I_old = I_new.copy()
t_old = t_new.copy()
k += 1
else:
one_more = False
def test_diffusion_exact_linear():
global L, beta, dx,
L = 1.5
beta = 0.5
N = 40
x = linspace(0, L, N+1)
dx = x[1] - x[0]
u = zeros(N+1)
U_0 = zeros(N+1)
U_0[0] = s(0)
U_0[1:] = u_exact(x[1:], 0)
dt = dx**2/(2*beta)
print 'stability limit:', dt
u, t = ode_FE(rhs, U_0, dt, T=1.2)
def test_diffusion_exact_linear():
global beta, dx, L, x # needed in rhs
L = 1.5
beta = 0.5
N = 4
x = linspace(0, L, N+1)
dx = x[1] - x[0]
u = zeros(N+1)
U_0 = zeros(N+1)
U_0[0] = s(0)
U_0[1:] = u_exact(x[1:], 0)
dt = 0.1
print dt
u, t = ode_FE(rhs, U_0, dt, T=1.2)
tol = 1E-12
for i in range(0, u.shape[0]):
diff = abs(u_exact(x, t[i]) - u[i,:]).max()
assert diff < tol, 'diff=%.16g' % diff
print 'diff=%g at t=%g' % (diff, t[i])
def test_diffusion_exact_linear():
global beta, dx, L, x # needed in rhs
L = 1.5
beta = 0.5
N = 4
x = np.linspace(0, L, N+1)
dx = x[1] - x[0]
u = np.zeros(N+1)
U_0 = np.zeros(N+1)
U_0[0] = s(0)
U_0[1:] = u_exact(x[1:], 0)
dt = 0.1
print(dt)
u, t = ode_FE(rhs, U_0, dt, T=1.2)
tol = 1E-12
for i in range(0, u.shape[0]):
diff = np.abs(u_exact(x, t[i]) - u[i,:]).max()
assert diff < tol, 'diff={:.16g}'.format(diff)
print('diff={:g} at t={:g}'.format(diff, t[i]))
L = 0.5
beta = 8.2E-5
N = 40
x = np.linspace(0, L, N + 1)
dx = x[1] - x[0]
u = np.zeros(N + 1)
U_0 = np.zeros(N + 1)
U_0[0] = s(0)
U_0[1:] = 283
dt = dx**2 / (2 * beta)
print('stability limit:', dt)
#dt = 0.00034375
from ode_system_FE import ode_FE
u, t = ode_FE(rhs, U_0, dt, T=1 * 60 * 60)
plt.ion()
y = u[0, :]
lines = plt.plot(x, y)
plt.axis([x[0], x[-1], 273, s(0) + 10])
plt.xlabel('x')
plt.ylabel('u(x,t)')
counter = 0
# Plot each of the first 100 frames, then increase speed by 10x
change_speed = 100
for i in range(0, u.shape[0]):
print(t[i])
plot = True if i <= change_speed else i % 10 == 0
lines[0].set_ydata(u[i, :])
if i > change_speed:
L = 1
beta = 1
N = 40
x = linspace(0, L, N+1)
dx = x[1] - x[0]
u = zeros(N+1)
U_0 = zeros(N+1)
U_0[0] = s(0)
U_0[1:] = 0
dt = dx**2/(2*beta)
print 'stability limit:', dt
t0 = time.clock()
from ode_system_FE import ode_FE
u, t = ode_FE(rhs, U_0, dt, T=1.2)
t1 = time.clock()
print 'CPU time: %.1fs' % (t1 - t0)
# Make movie
import os
os.system('rm tmp_*.png')
import matplotlib.pyplot as plt
plt.ion()
y = u[0,:]
lines = plt.plot(x, y)
plt.axis([x[0], x[-1], -0.1, 1.2*s(0)])
plt.xlabel('x')
plt.ylabel('u(x,t)')
counter = 0
# Plot each of the first 100 frames, then increase speed by 10x
beta = 8.2E-5
N = 40
x = linspace(0, L, N+1)
dx = x[1] - x[0]
u = zeros(N+1)
U_0 = zeros(N+1)
U_0[0] = s(0)
U_0[1:] = 283
dt = dx**2/(2*beta)
print 'stability limit:', dt
#dt = 0.00034375
t0 = time.clock()
from ode_system_FE import ode_FE
u, t = ode_FE(rhs, U_0, dt, T=1*60*60)
t1 = time.clock()
print 'CPU time: %.1fs' % (t1 - t0)
# Make movie
import os
os.system('rm tmp_*.png')
import matplotlib.pyplot as plt
plt.ion()
y = u[0,:]
lines = plt.plot(x, y)
plt.axis([x[0], x[-1], 273, s(0)+10])
plt.xlabel('x')
plt.ylabel('u(x,t)')
counter = 0
# Plot each of the first 100 frames, then increase speed by 10x