Numerical Integration Using Simpson 1/3 Method Algorithm

In numerical analysis, Simpson's 1/3 rule (method) is a technique for approximating definite integral.

This method is based on Newton's Cote Quadrature Formula and Simpson 1/3 rule is obtained when we put value of n = 2 in this formula.

In this article, we are going to develop an algorithm for Simpson 1/3 Rule.

Simpson's 1/3 Rule Algorithm

1. Start

2. Define function f(x)

3. Read lower limit of integration, upper limit of 
   integration and number of sub interval

4. Calcultae: step size = (upper limit - lower limit)/number of sub interval

5. Set: integration value = f(lower limit) + f(upper limit)

6. Set: i = 1

7. If i > number of sub interval then goto 

8. Calculate: k = lower limit + i * h

9. If i mod 2 =0 then 
     Integration value = Integration Value + 2* f(k)
   Otherwise
     Integration Value = Integration Value + 4 * f(k)
   End If

10. Increment i by 1 i.e. i = i+1 and go to step 7

11. Calculate: Integration value = Integration value * step size/3 

12. Display Integration value as required answer

13. Stop

Recommended Readings

  1. Numerical Integration Trapezoidal Method Algorithm
  2. Numerical Integration Using Trapezoidal Method Pseudocode
  3. Numerical Integration Using Trapezoidal Method C Program
  4. Trapezoidal Rule Using C++ with Output
  5. Numerical Integration Using Simpson 1/3 Method Algorithm
  6. Numerical Integration Using Simpson 1/3 Method Pseudocode
  7. Numerical Integration Using Simpson 1/3 Method C Program
  8. Simpson 1/3 Rule Using C++ with Output
  9. Numerical Integration Using Simpson 3/8 Method Algorithm
  10. Numerical Integration Using Simpson 3/8 Method Pseudocode
  11. Numerical Integration Using Simpson 3/8 Method C Program
  12. Simpson 3/8 Rule Using C++ with Output