Implicit Scheme: error type : ValueError : x and y must have same first dimension

Question

I am trying to implement a heat equation solver using the Euler scheme for time integration, here is the particular equation implemented:

And here is my code:

Nt = 20
Nx = 100
x = np.linspace(0,1,Nx+1)
t = np.linspace(0,1,Nt+1)

dx = 1/Nx
dt = 1/Nt
F = dt/(dx**2)



T_temps = np.zeros(Nx+1)
T = np.zeros(Nx+1)

for i in range(Nx+1):
    T_temps[i] = np.sin(x[i])

for n in range(0,Nt):
    for i in range(1,Nx):
        T[i] = T_temps[i] + F*(T_temps[i-1]-2*T_temps[i]+T_temps[i+1]) + ((np.pi**2)-1)*np.exp(-t[i])*np.sin(x[i])
    T[0] = 0.
    T[Nx] = 0.

    T_temps[:] = T
    
plt.plot(t,T)
plt.show()

It works when the two values of Nt and Nx are the same but when I have to modify the value of Nt for the exercise that've to do it générâtes this error:

ValueError: x and y must have same first dimension, but have shapes (101,) and (21,)

I Don't know how to deal with it: I understand the meaning but I Don't know how to avoid it?

Thaks a lot for your help,

Best regards,

Answer 1

When I wanted to reproduce I hit index error. In np.exp(-t[i]) should be np.exp(-t[n]) . Then the whole line will be:

T[i] = T_temps[i] + F * (T_temps[i - 1] - 2 * T_temps[i] + T_temps[i + 1]) + ((np.pi ** 2) - 1) * np.exp(-t[n]) * np.sin(x[i])

You are trying to plot, 21 number (shape of t ) in relation to 101 numbers (shape of T ). To solve, change to plt.plot(x, T) as x and T has the same shape.