问索引错误:索引2超出了大小为2的轴0的边界

EN

def f(t,x,y):
    xprime = x - y + (2*t) - (t**2) - (t**3)
    return xprime

def g(t,x,y):
    yprime = x + y - (4*(t**2)) + (t**3)
    return yprime


#Exact Solution
def exact(t):
    y = np.zeros(len(t))
    x = np.zeros(len(t))
    
    for i in range(n):
        cos_arr = np.cos(t)
        sin_arr = np.sin(t)
        
        y = np.exp(t) * cos_arr + t**2
        x = np.exp(t) * sin_arr - t**3
        
        return x, y
    
 #Explicit Euler   
def Eulerx(t0, tmax, x0, n):
    t, dt = np.linspace(t0, tmax, n, retstep = True)
    x = np.zeros(n)
    y = np.zeros(n)
    x[0] = x0
    y[0] =y0
    for i in range (n-1):
        x[i+1] = x[i] + (dt/2) * f(t[i], x[i], y[i])
        return t, x

#RK2
        
def RK2x(t0, tmax, x0, n):
    t, dt = np.linspace(t0, tmax, n, retstep = True)
    x = np.zeros(n)
    y = np.zeros(n)
    x[0] = x0
    y[0]=y0
    for i in range(n-1):
        xK1 = f(t[i], x[i],y[i])
        xK2 = f(t[i]+ dt, x[i] +dt * xK1, y[i])
        x[i+1] = x[i] +(dt* (1/2)*(xK1 + xK2))
        return t, x
    

    
#Classical RK4

def RK4x(t0, tmax, x0, n):
    t, dt = np.linspace(t0, tmax, n, retstep = True)
    x = np.zeros(n)
    y = np.zeros(n)
    x[0] = x0
    y[0] =y0
    for i in range(n-1):
        x4K1 = f(t[i],x[i],y[i])
        x4K2 = f(t[i]+((1/2)*dt), x[i]+ ((1/2)*dt*x4K1),y[i])
        x4K3 = f(t[i] +((1/2)*dt), x[i] + ((1/2)*dt*x4K2),y[i])
        x4K4 = f(t[i]+dt, x[i]+dt*x4K3,y[i])
        x[i+1] = x[i] + (dt*(1/6)*(x4K1 + (2* x4K2) +(2*x4K3) +x4K4))
        
        return t, x
    

    
if __name__ == '__main__': 
    t0 = 0
    tmax = 1
    x0 = 1
    y0 = 0
    n=50
    
    [t,X1] = Eulerx(t0,tmax, x0,n)
    [t,Y1] = Eulery(t0,tmax, y0,n)
    
    [t, X2]= RK2x(t0,tmax, x0,n)
    [t, Y2]= RK2y(t0,tmax, y0,n)
    
    [t, X3]= RK4x(t0,tmax, x0,n)
    [t, Y3]= RK4y(t0,tmax, y0,n)
    
    x=exact(t)
    y=exact(t)
    
    abs_errx1= abs(x-X1)
    abs_errx2= abs(x-X2)
    abs_errx3= abs(x-X3)

    
    
    

    
    print("=========================================================================")
    print(" n        Eulerx     Eulery      RK2x      RK2y      RK4x      RK4y", end='\n')
    for i in range(n):
        print(abs_errx1[i], abs_erry1[i], abs_errx2[i], abs_erry2[i], abs_errx3[i], abs_erry3[i])
    print("=========================================================================")