dx = 0.1
dy = 0.1
Nx = int(1 + (Lx/dx))
Ny = int(1 + (Ly/dy))
nx = Nx-2
ny = Ny-2
d2dx = 1/(dx*dx)
u = np.zeros(Nx*Ny)
f = np.zeros(Nx*Ny)
i = 0
for j in range(Ny):
u[i+j*Nx] = 1
u = pde.jacobi(u,f,dx,Nx,Ny,1000)
u_int = np.zeros(nx*ny)
for j in range(ny):
for i in range(nx):
u_int[i+j*nx] = u[(i+1) + (j+1)*Nx]
u_plot = np.zeros([Nx,Ny])
for j in range(Ny):
for i in range(Nx):
u_plot[i,j] = u[i+j*Nx]
x = np.zeros([Nx+1,Ny+1])
y = np.zeros([Nx+1,Ny+1])
for j in range(Ny+1):
for i in range(Nx+1):
f[i + j*Nx] = 1
# boundary conditions
for j in range(Ny):
i = 0
T[i+j*Nx] = 1
i = Nx-1
T[i+j*Nx] = 0
for i in range(Nx):
j = 0
T[i+j*Nx] = 0
j = Ny-1
T[i+j*Nx] = 0
# Jacobi iteration
T = pde.jacobi(T,f,dx,Nx,Ny,1000)
# check error
# (build matrix)
nx = Nx - 2
ny = Ny - 2
A = np.zeros([nx*ny,nx*ny])
for q in range(nx*ny):
for p in range(nx*ny):
if p == q:
A[p,q] = -4*d2dx2
elif p == q-1:
A[p,q] = 1*d2dx2
elif p == q+1:
A[p,q] = 1*d2dx2
elif p == q-nx: