我发现您的实施存在一些问题：

• 替换为（在您的代码和问题中），否则没有任何意义！$t$$dt$
• 方程的第二部分（带有和之间存在混合。此外，您的通量评估是错误的：例如应该阅读。$a$$F$$f$Fplus0.5*Up**2
• 在 U 的计算中Un-Um和周围也缺少括号。Um-Up

我已经基于http://folk.ntnu.no/leifh/teaching/tkt4140/._main075.html实施了 Lax-Wendroff 方案，它似乎工作正常。

以下代码将您的实现与各种修复和新修复进行了比较。两者都有效并给出相同的结果。

import numpy as np
import matplotlib.pyplot as plt

Nx=100;Nt=100;t_end=2.0
nChoice = 1

### LAX-WENDROFF SCHEME with periodic BCs
Nx = Nx+1                         # Number of grid points
xmax = 1.                         # Domain limit to the right
xmin = 0.                         # Domain limit to the left
h = (xmax-xmin)/(Nx-1)           # Mesh size
x = np.arange(xmin,xmax,h)       # Discretized mesh
U =  np.exp(-10*(4*x-1)**2)       # Initial solution
dt = 1.0/Nt                        # Time step
t = 0.                            # Initial time

aplus, aminus, Fplus, Fminus, Fn = (np.zeros(Nx-1) for i in range(5))
nsteps = 0
while (t <= t_end):
    if np.any(np.isnan(U)):
      raise Exception('NaNs detected --> exit')
      
    if nChoice==0: # your implementation
        v = dt/(2*h)
        a = (dt**2)/(2*h**2)
        Un = U
        Um = np.roll(Un,1)
        Up = np.roll(Un,-1)
        # F_plus  = 0.5 * (Up + Un)
        # F_minus = 0.5 * (Un + Um)
        F_plus = 0.5*Up**2
        F_minus = 0.5*Um**2
        Fn = 0.5*Un**2
        # U =  Un - v * (Um-Up) + a * (F_plus  * Un-Um - F_minus *Um-Up)
        U =  Un - v*(F_plus-F_minus) + a*( 0.5*(Up+U)*(F_plus-Fn)- 0.5*(U+Um)*(Fn-F_minus))
      
    else: # another implementation
        aplus[:-1] = 0.5 * (U[:-1] + U[1:])
        aplus[-1]  = 0.5 * (U[-1]  + U[0])
        aminus[1:] = aplus[:-1]
        aminus[0]   = aplus[-1]
        
        Fn[:] = 0.5*U**2
        Fplus[:-1] = Fn[1:] # or just use np.roll as you did
        Fplus[-1]  = Fn[0]
        Fminus[1:] = Fn[:-1]
        Fminus[0]  = Fn[-1]
        
        U[:] = U - dt/(2*h)*(Fplus-Fminus) + (dt**2)/(2*h**2)*(aplus*(Fplus-Fn) - aminus*(Fn-Fminus))
    
    t = t+dt
    nsteps+=1  
    
    # plot solution evolution every 10 time steps
    if np.mod(nsteps,10)==1 or t>=t_end:
        plt.figure()
        plt.plot(x,U)
        plt.title('t={:.2f}'.format(t),fontsize=16)
        plt.xlabel('x',fontsize=18)
        plt.ylabel('u',fontsize=18)
        plt.grid()
        plt.ylim(0,1)
        plt.show()
```