用python(NumPy)求解热方程

我解决了金属棒的热方程,一端保持在100°C,另一端保持在0°C

import numpy as np
import matplotlib.pyplot as plt

dt = 0.0005
dy = 0.0005
k = 10**(-4)
y_max = 0.04
t_max = 1
T0 = 100

def FTCS(dt,dy,t_max,y_max,k,T0):
    s = k*dt/dy**2
    y = np.arange(0,y_max dy,dy) 
    t = np.arange(0,t_max dt,dt)
    r = len(t)
    c = len(y)
    T = np.zeros([r,c])
    T[:,0] = T0
    for n in range(0,r-1):
        for j in range(1,c-1):
            T[n 1,j] = T[n,j]   s*(T[n,j-1] - 2*T[n,j]   T[n,j 1]) 
    return y,T,r,s

y,s = FTCS(dt,T0)

plot_times = np.arange(0.01,1.0,0.01)
for t in plot_times:
    plt.plot(y,T[t/dt,:])

如果改变Neumann边界条件,一端是绝缘的(不是焊剂),

那么,计算期限如何

T[n 1,j 1])

应该修改？

解决方法

for j in range(1,c-1):
    T[n 1,j 1])  # as before
j = c-1 
T[n 1,j-1])  # note the last term here