Python Program for implementation of Simpson's rule

In this, program uses Simpson's 1/3 rule to determine the approximate number for combining numbers in the Python programming.

Simpson's System 1/3 Python Method

In this python system, the lower_limit and upper_limit are the lower and upper limit of a integration, sub_interval is the minimum number used when finding the sum and function f (x) to be combined in the simulation of Simpson 1/3 defined using python.

Implementation

For the implementation you have to write a function called simps that takes the input parameters f, a, b and N and returns the approximation. In addition, let us provide the default value of N.

scipy.integrate.simps

The SciPy 

scipy.integrate subpackage includes many functions for approximation integral and numerically solved different equations.

 

Let's import the subpackage as name spi.

import scipy.integrate as spi

The scipy.integrate.simps function computes a approximation of a definite integral by the of Simpson rule. scipy.integrate.simps returns approxiamtion of the integral using Simpson's rule.

Example 1: Write a program for the implementation of 1/x

Python code:

from scipy.integrate import simps
import numpy as np
import scipy.integrate as spi
N = 8
a = 1
b = 2
x = np.linspace(a,b,N)
y = 1/x
appoximation = spi.simps(y,x)
print(appoximation)
Output:
0.6933892496392496

Example 2: Write a program for the implementation of x2
Python code:
from scipy.integrate import simps
import numpy as np
import scipy.integrate as spi
N = 8
a = 1
b = 2
x = np.linspace(a,b,N)
y = x**2
appoximation = spi.simps(y,x)
print(appoximation)
Output:
2.3338192419825075