Composite Simpson 1/3 Rule

  Algorithm : Composite Simpson’s (1/3)rd rule

Composite_simpson’s(a,b,n)
	{
	//Let us consider a function f(x). We want to find the integrating value
 of f(x) w.r.t. x  from lower limit ‘a’ to upper limit ‘b’ with subdivision n.

	h=(b-a)/n
	x=a
	sum=0
	for(i=1 to n-1)
		{
		if(i%2==0)
      		{
      		x=a+i*h;
      		sum=sum+(2*h/3)*f(x);	     //f(x) is a function 
      		}			       which  returns the 
    		else			       value of f(x) at x=x
      		{
      		x=a+i*h;
      		sum=sum+(4*h/3)*f(x);
      		}	
}				 
	r=h/3*[f(a)+f(b)]+sum	 
	print “r”
}						


C Program For Composite Simpson 1/3 Rule

Source Code:

#include>stdio.h>
#include>conio.h>
#include>math.h>

void simpson(float,float,int);
float f(float);
void main()
{
 int n;
 float a,b;
 clrscr();
 printf("\nCALCULATE :\n");
 printf("\n%c\n%cx^3.dx     using the given limits.\n",244,245);
 printf("\nEnter the upper limit of the function:");
 scanf("%f",&b);
 printf("\nEnter the lower limit of the function:");
 scanf("%f",&a);
 printf("\nENTER THE NUMBE3R OF SUB-DIVISIONS(must be even):");
 scanf("%d",&n);
 simpson(a,b,n);
 getch();
}

void simpson(float a,float b,int n)
{
 float h,sum1=0,x,R,sum2=0;
 int i;
 h=(b-a)/n;
 x=a;
 for(i=1;i<=n-1;i++)
 {
  x=a+i*h;
  if(i%2==0)
  {
   sum1=sum1+f(x);
  }
  if(i%2!=0)
  {
   sum2=sum2+f(x);
  }
 }
 R=(h/3)*(f(a)+f(b))+4*(h/3)*sum2+2*(h/3)*sum1;
 printf("\n\nValue=%f",R);
 }

float f(float x)
{
 return (x*x*x);
}