CPNM LAB PROGRAM-13

 

13. Implement Simpson’s rule for numerical integration

         FLOW CHART :-

ALGORYTHMS :-

Step – 1 : Start 

Step – 2 : Declare i, n as integers 

Step – 3 : Declare s1 = 0, s2 = 0, a, b, h, x, integral as float variables 

Step – 4 : Read a, b 

Step – 5 : Enter the number of steps i.e., value of n 

Step – 6 : Assign h = (b – a)/n 

Step – 7 : Assign x = a 

Step – 8 : Initialize i = 1 

Step – 9 : If i < n condition is true go to Step–10 else Step–15 

Step – 10 : Assign x += h 

Step – 11 : If(i % 2 == 0) go to Step–12 else go to Step–13 

Step – 12 : Assign s1 += 2 * f(x) 

Step – 13 : Assign s2 += 4 * f(x) 

Step – 14 : Increment i value and go to Step–9 

Step – 15 : Assign integral value i.e, integral = (h/3) * (f(a) + s1 + s2 + f(b)) 

Step – 16 : Print the values of integral Step – 17 : Stop 

PROGRAM :-

#include<stdio.h>

#include<conio.h>

#include<stdlib.h>

#include<math.h>

float f(float x)

{

return(1/(1 + x));

}

main()

{

int i, n;

float s1 = 0, s2 = 0, a, b, h, x, integral;

clrscr();

printf("Enter a and b limits \n");

scanf("%f,%f",&a,&b);

printf("Enter no. of steps : \n");

scanf("%d",&n);

h = (b - a) / n;

x = a;

for(i = 1; i < n; i++)

{

x += h;

if(i % 2 == 0)

s1 += 2 * f(x);

else

s2 += 4 * f(x);

}

integral = (h / 3) * (f(a) + s1 + s2 + f(b));

printf("Integral is %f",integral);

getch();

return 0;

}

OUTPUT:-

Run 1:

Enter a and b limits

2,4

Enter no. of steps :

2

Integral is 0.511111

Run 2:

Enter a and b limits

5,7

Enter no. of steps :

5

Integral is 0.270600