Python 用Euler和Runge_-Kutta方法求解二阶微分方程

我试图用Euler和Range-Kutta方法解决一个弹簧质量问题，并比较图。我已经为Euler和Runge Kutta编写了函数，但是在调用函数解决我的问题之后，我的图似乎没有显示任何数据。请帮助我修复绘图，并检查我的代码中是否有任何错误，谢谢

#function Euler
def euler ( y, t, dt, derivative):
    y_next = y + derivative(y, t) * dt
    return y_next

# function Runge-Kutta
# 2nd order Runge-Kutta method routine

def Runge_Kutta (y, time, dt, derivative):
    k0 = dt * derivative (y, time)
    k1 = dt * derivative (y + k0, time + dt)
    y_next = y + 0.5 * (k0 + k1)
    return y_next

这就是我试图解决的问题

[![""" A spring and mass  system. the coefficient of friction \mu is not negligible.generate a position vs. time plot for the motion of the mass, given an initial displacement x = 0.2m , spring constant k = 42 N/m , mass m =0.25 Kg, coefficient of friction \mu = 0.15 and initial velocity v = 0

F = -kx +/-mu mg """


from pylab import *
from Runge_Kutta_routine import Runge_Kutta
from eulerODE import euler

N = 500      #input ("How many number of steps to take?")
x0 = 0.2
v0 = 0.0
tau = 3.0     #input ("What is the total time of the simulation in seconds?")
dt = tau /float ( N-1)

k = 41.0      #input (" what is the spring constant?")
m = 0.25      #input ("what is the mass of the bob?")
gravity = 9.8
mu = 0.15     #input ("what is the coefficient of friction?")

""" we create a Nx2 array for storing the results of our calculations. Each 2- element row will be used for the state of the system at one instant, and each instant is separated by time dt. the first element in each row will denote position, the second would be velocity"""

y = zeros (\[N,2\])

y \[0,0\] = x0
y \[0,1\] = v0

def SpringMass (state, time):
    """ we break this second order DE into two first order DE introducing dx/ dt = v & dv/dt = kx/ m +/- mu g....

Note that the direction of the frictional force changes depending on the sign of the velocity, we handle this with an if statement."""


    g0 = state\[1\]
    if g0 > 0:
        g1 = -k/m * state \[0\] - gravity * mu
    else:
        g1 = -k/m * state \[0\] + gravity * mu

    return array (\[g0, g1\])

# Now we do the calculations
# loop only N-1 so that we don;t run into a problem addresssing y\[N+1\] on the last point

    for j in range (N-1):
        #y \[j+1\] = euler ( y\[j\] , 0, dt, SpringMass)
        y \[j+1\] = Runge_Kutta ( y\[j\], 0 , dt, SpringMass)

# Now we plot the result

time = linspace ( 0 , tau, N)
plot ( time, y\[:,0\], 'b-', label ='position')

xlabel('time')
ylabel('position')


show()][1]][1] 

---

看起来您的循环从范围（N-1）中j的

开始：

计算数组

y

是缩进的，因此Python认为这些行是函数

SpringMass

的一部分。由于这些行位于

return

语句之后，因此它们永远不会执行

要更正此问题，请移动这些行，使的

行没有缩进，而其他行只有四个缩进空间。看看这是否解决了你的问题

请注意，此处编写的代码仍然无法工作。在方括号之前有多余的反斜杠，在一个未命名的模块中编写
Euler
和
Runge_Kutta
函数，但主代码希望它们在两个不同的模块中，等等。还有许多错误样式的示例。这些问题可能就是你还没有得到任何（其他）答案的原因。在这里发布之前，帮自己一个忙并清理代码。
您是否尝试过打印这些值，例如，查看它们是否为NaN或infinity？