将上述代码中的边界条件改成\phi _{B}^{n+1} =(1-\lambda )\phi _{B}^{n} +\lambda \phi _{B-1}^{n+1}

好的，将上述代码中的边界条件改成 $\phi _{B}^{n+1} =(1-\lambda )\phi _{B}^{n} +\lambda \phi _{B-1}^{n+1}$，则代码如下：

import numpy as np

# Parameters
L = 1.0     # Length of the domain
N = 100     # Number of grid points
dx = L/N    # Grid spacing
D = 1.0     # Diffusion coefficient
T = 0.5     # Total time
dt = 0.4*dx**2/(2*D)  # Time step size
nt = int(T/dt) + 1    # Number of time steps

# Initial condition
x = np.linspace(0, L, N+1)
phi0 = np.sin(np.pi*x)

# Boundary conditions
phiL = 0.0
phiR = 0.0

# Solve the diffusion equation
phi = phi0.copy()
for n in range(nt):
    # Apply boundary conditions
    phi[0] = phiL
    phi[-1] = (1 - dt*D/dx**2)*phi[-1] + dt*D/dx**2*phi[-2]
    # Update the solution at interior points
    for i in range(1, N):
        phi[i] = phi[i] + dt*D/dx**2*(phi[i+1] - 2*phi[i] + phi[i-1])
        
# Plot the solution
import matplotlib.pyplot as plt
plt.plot(x, phi0, label='Initial condition')
plt.plot(x, phi, label='Final solution')
plt.legend()
plt.xlabel('x')
plt.ylabel('phi')
plt.show()

这里我们将右边界的边界条件改成了 $\phi _{B}^{n+1} =(1-\lambda )\phi _{B}^{n} +\lambda \phi _{B-1}^{n+1}$。