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Program to implement NEWTON'S FORWARD METHOD OF INTEROLATION.


   

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

void main()
{
int n;                          // no. of terms.
int i,j;                        // Loop variables
float ax[10];                   // 'X' array limit 9
float ay[10];                   // 'Y' array limit 9
float x;                        // User Query for what value of X
float y=0;                      // Calculated value for coressponding X.
float h;                        // Calc. Section
float p;                        // Calc. Section
float diff[20][20];             // to store Y
float y1,y2,y3,y4;              // Formulae variables.

clrscr();
printf("\t\t !! NEWTON'S GREGORY FORWARD INTERPOLATION FORMULA !! ");
// Input section.
printf("\n\n Enter the no. of terms -> ");
scanf("%d",&n);

// Input Sequel for array X
printf("\n\n Enter the value in the form of x -> ");
// Input loop for X.
for(i=0;i<n;i++)
   {
   printf("\n Enter the value of x%d -> ",i+1);
   scanf("%f",&ax[i]);
   }

// Input sequel for array Y.
printf("\n\n Enter the value in the form of y -> ");
// Input loop for Y.
for(i=0;i<n;i++)
   {
   printf("\n Enter the value of y%d -> ",i+1);
   scanf("%f",&ay[i]);
   }

// Inputting the required value quarry
printf("\n\n Enter the value of x for ");
printf("\n which u want the value of y -> ");
scanf("%f",&x);

// Calculation and processing section.
h=ax[1]-ax[0];

// for 1.
for(i=0;i<n-1;i++)
   diff[i][1]=ay[i+1]-ay[i];
// for 2, 3, 4
for(j=2;j<=4;j++)
   for(i=0;i<n-j;i++)
      diff[i][j]=diff[i+1][j-1]-diff[i][j-1];

do
 {
 i++;
 }
 while(ax[i]<x);
i--;

p=(x-ax[i])/h;
y1=p*diff[i-1][1];                                            // 1
y2=p*(p+1)*diff[i-1][2]/2;                                    // 2
y3=p*(p+1)*(p-1)*diff[i-2][3]/6;                              // 3
y4=(p+2)*(p+1)*p*(p-1)*diff[i-3][4]/24;

// Taking sum
y=ay[i]+y1+y2+y3+y4;

// Outut Section
printf("\n When x = %6.4f , y = %6.8f",x,y);

// Invoke user watch halt function
printf("\n\n\n\t\t\t !! PRESS ENTER TO EXIT !! ");


getch();
}
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