Gauss Central Difference formula

/*      The following C program implements Gauss Central Difference Formula in

         estimating functional values near the middle part of a given table. The tabular

         values (abscissa and ordinate) are read as input.         */

  

#include<stdio.h>

#include<conio.h>

#define max 30

void main()

{

 float table[max][max];

 int count, mid, i, j;

 float x, n, h, y, p ;

 /* Setting all the contents of the table to zero */

 for(i=0; i<max; i++)

 for(j=0; j<max; j++)

  table[i][j]=0;

 printf("\n How many values are to be entered? \n");

 scanf("%d",&count);

 printf("\n Enter the values of x and y in tabular format: \n\n");

 for(i=0; i<=2*count-2; i+=2)

 for(j=0; j<=1; j++)

 scanf("%f",&table[i][j]) ;

 printf("\n Find the value of y at x = ? \n");

 scanf("%f",&x);

 /* constructing the central difference table */

 for(i=2; i<=count; i++)

 for(j=i-1, n=1; n<=count+1-i; j+=2, n++)

 {

  table[j][i]=table[j+1][i-1] - table[j-1][i-1];

 }

 

/* Finding the middle of the x column of the table */

 if(count%2==1)

            mid=count-1;

 else

mid=count;

 h=table[mid+2][0] - table[mid][0] ;

 n=p=(x-table[mid][0])/h;

 /* Using interpolation formula */

 if(x>table[mid][0])

 {

  printf("\n APPLYING GAUSS FORWARD CENTRAL

                  DIFFERENCE FORMULA   \n");

  y=table[mid][1] + n*table[mid+1][2];

  for(i=3; i<=count; i++)

            if(i%2==1)

              {

              n*=(p-(int)i/2)/(i-1);

              y+=n*table[mid][i];

              }

            else

              {

              n*=(p+(int)i/2 -1)/(i-1);

              y+=n*table[mid+1][i];

              }

 }

 else

 {

  printf("\n------ APPLYING GAUSS BACKWARD CENTRAL DIFFERENCE FORMULA ------\n");

  y=table[mid][1] + n*table[mid-1][2];

  for(i=3; i<=count; i++)

            if(i%2==1)

              {

              n*=(p+(int)i/2)/(i-1);

              y+=n*table[mid][i];

              }

            else

                                                                                                                                                                                              {

              n*=(p-(int)i/2 +1)/(i-1);

              y+=n*table[mid-1][i];

              }

 }

 /* printing the central difference table */

 printf("\n CENTRAL DIFFERENCE TABLE   \n");

 for(i=0; i<=2*count-2; i++)

 {

  if(i%2==0)

            printf("%2.3f %2.3f",table[i][0], table[i][1]);

  else

            printf("           ");

  for(j=2; j<=count; j++)

            if((j%2==0 && i%2==1) || (j%2==1 && i%2==0))

            {

             if(i>=j-1 && i<2*count-j)

                         printf(" %2.3f",table[i][j]);

            }

            else

             printf("     ");

  printf("\n");

 }

  printf("\n\n At x=%f,  y=%f \n",x,y);

  getch();

}

 

SAMPLE OUTPUT:

Evaluating the value of y at x = 0.425, given the following table of values:

x	0.0	0.2	0.4	0.6	0.8
y	0.0000	0.1823	0.3365	0.4700	0.5878