Trying to use Simpson's Law in Python

December 29, 2022

I am trying to write a program about Simpson’s Law.What I am trying to do is use as error as shown in this picture:

In the code i write the Ih is my f1 and Ih/2 is my f2.If the error doesnt happen then the steps get halved.

However I get this error

Traceback (most recent call last):
  File "C:\Users\Egw\Desktop\Analysh\Askhsh1\example.py", line 22, in <module>
    sim2 = simps(f2, x2)
  File "C:\Users\Egw\Desktop\Analysh\Askhsh1\venv\lib\site-packages\scipy\integrate\_quadrature.py", line 436, in simps
    return simpson(y, x=x, dx=dx, axis=axis, even=even)
  File "C:\Users\Egw\Desktop\Analysh\Askhsh1\venv\lib\site-packages\scipy\integrate\_quadrature.py", line 542, in simpson
    last_dx = x[slice1] - x[slice2]
IndexError: index -1 is out of bounds for axis 0 with size 0

Process finished with exit code 1

My code is

import numpy as np
from sympy import *
from scipy.integrate import simps

a = 0
b = np.pi * 2
N = 100
ra = 0.1 # ρα
R = 0.05
fa = 35 * (np.pi/180) # φα
za = 0.4
Q = 10**(-6)
k = 9 * 10**9
aa = sqrt(ra**2 + R**2 + za**2)
error = 5 * 10**(-9)

while True:
    x1 = np.linspace(a, b, N)
    f1 = 1 / ((aa ** 2 - 2 * ra * R * np.cos(x1 - fa)) ** (3 / 2))
    sim1 = simps(f1, x1)
    x2 = np.linspace(a, b, int(N/2))
    f2 = 1 / ((aa ** 2 - 2 * ra * R * np.cos(x2 - fa)) ** (3 / 2))
    sim2 = simps(f2, x2)
    if abs(sim1 - sim2) < error:
        break
    else:
        N = int(N/2)

print(sim1)

I wasnt expecting any error,and basically expecting to calculate correctly.

>Solution :

When you reduce the grid step by half h -> h/2, the number of grid steps in turn grows N -> 2 * N, so you have to make two changes in your code:

Define x2 to have twice as many elements as x1

   x2 = np.linspace(a, b, 2 * N)

Update N to be twice it was on the previous iteration

        N = 2 * N

The resulting code would be

import numpy as np
from sympy import *
from scipy.integrate import simps

a = 0
b = np.pi * 2
N = 100
ra = 0.1 # ρα
R = 0.05
fa = 35 * (np.pi/180) # φα
za = 0.4
Q = 10**(-6)
k = 9 * 10**9
aa = sqrt(ra**2 + R**2 + za**2)
error = 5 * 10**(-9)

while True:
    x1 = np.linspace(a, b, N)
    f1 = 1 / ((aa ** 2 - 2 * ra * R * np.cos(x1 - fa)) ** (3 / 2))
    sim1 = simps(f1, x1)
    x2 = np.linspace(a, b, 2 * N)
    f2 = 1 / ((aa ** 2 - 2 * ra * R * np.cos(x2 - fa)) ** (3 / 2))
    sim2 = simps(f2, x2)
    if abs(sim1 - sim2) < error:
        break
    else:
        N = 2 * N

print(sim1)

And this prints the value