def finite_difference(L, Nx, N, dt, C, P_L, P_R):
x = linspace(0, L, Nx+1)
dx = x[1] - x[0]
C = 0.4*C*dt/(dx**2)
print C
Q = zeros(Nx+1)
Q_1 = P_R**2*ones(Nx+1)
for n in range(0, N):
# Compute u at inner mesh points
for i in range(1, Nx):
Q[i] = Q_1[i] + C*(Q_1[i-1]**2.5 - 2*Q_1[i]**2.5 + Q_1[i+1]**2.5)
# Insert boundary conditions
Q[0]=P_L**2; Q[Nx]=P_R**2
# Update u_1 before next step
Q_1[:]= Q
return sqrt(Q), x
def finite_difference(L, Nx, N, dt, C, P_L, P_R):
x = linspace(0, L, Nx+1)
dx = x[1] - x[0]
C = C*dt/(dx**2)
print C
P = zeros(Nx+1)
P_1 = P_R*ones(Nx+1)
for n in range(0, N):
# Compute u at inner mesh points
for i in range(1, Nx):
#print P_1
P[i] = P_1[i] + C*(P_1[i-1]**2 - 2*P_1[i]**2 + P_1[i+1]**2)
# Insert boundary conditions
P[0]=P_L; P[Nx]=P_R
# Update u_1 before next step
P_1[:]= P
return P, x
