Error with list index out of range

Question

It's uncomfortable code, I know, and sorry. Especially, if it's a stupid question.

Here is an error with list, and I don't know why (I'm beginner). Can someone, please, tell me, how to fix it?

This is the output:

Traceback (most recent call last):
  File "C:/Users/milom/PycharmProjects/ChislM/method.py", line 77, in <module>
    vx, vy = rk3(diff1, 0, U0, 10, 100)
  File "C:/Users/milom/PycharmProjects/ChislM/method.py", line 39, in rk3
    x,v=step(f, h, i, x0, U0)
  File "C:/Users/milom/PycharmProjects/ChislM/method.py", line 11, in step
    k2 = f(x[i] + (1 / 3) * h[i], v[i] + (1 / 3) * k1)
IndexError: list index out of range

Code:

import matplotlib.pyplot as plt
import math as m
import pandas as pd

x =[0]*101
v =[0]*101

def step(f, h, i, x0, U0):
    x[0] = x0
    v[0] = U0
    k1 = f(x[i], v[i])
    k2 = f(x[i] + (1 / 3) * h[i], v[i] + (1 / 3) * k1)
    k3 = f(x[i] + (2 / 3) * h[i], v[i] + (2 / 3) * h[i] * k2)
    x[i] = x[i - 1] + h[i]
    v[i] = v[i - 1] + (h[i]) * ((1 / 4) * k1 + (3 / 4) * k3)
    return x, v


def rk3(f, x0, U0, x1, n):
    h = [(x1 - x0) / float(n)]
    for i in range(1, n+1):
        x,v=step(f, h, i, x0, U0)
        ###h= control(f, h[i], i, v[i], x0, U0)
    return x, v


def diff1(x, U):
    return 0.1


def diff(x, U):
    return -(m.cos(10 * x) + ((m.log(1 + x ** 2)) / (1 + x)) * (U ** 2) + U)


def exact_path():
    plt.grid()
    plt.plot(vx, vy)
    plt.show()


def table():
    mytable = pd.DataFrame({
        'Xn': vx,
        'Vn': vy,
    }, index=[i for i in range(0, 101)])
    mytable.index.name = 'number'
    pd.set_option('display.max_rows', None)
    print(mytable)


task = int(input("Task:"))
U0 = float(input("First value- U0:"))

if task == 2:
    vx, vy = rk3(diff, 0, U0, 10, 100)
    table()
    exact_path()

if task == 1:
    vx, vy = rk3(diff1, 0, U0, 10, 100)
    table()
    exact_path()

PS It's a simple 3th order Runge-Kutta method, but mostly problem with synthax. I tried to implement method with Python.

Answer 1

In the rk3() function you have h = [(x1 - x0) / float(n)] which creates an list with only a single element in it. This means that the only valid non-negative index that can be used with it would be h[0] —and an attempt to use any other index value, as is likely in the step() function in the for loop, will cause an IndexError .