BACKWARD DIFFERENCE TABLE USING C PROGRAMMING

TITLE: 

TO GENERATE THE BACKWARD DIFFERENCE TABLE USING C PROGRAMMING

OBJECTIVES:

• To be able to follow the algorithm of Newton's Backward Interpolation method to generate backward difference table.

• To build some programming concepts by solving practical problems.

 TOOLS REQUIRED:

• Computer workstation

• Program software (as necessary)

 THEORY:

While interpolating intermediate value of dependent variable for equi-spaced data of independent variable, at the end of the table, Newton's Backward Interpolation formula is used. 

 ALGORITHM:

1. Start

2. Read the number of data n and the datas.

3. Set i=1

TITLE: 

TO GENERATE THE BACKWARD DIFFERENCE TABLE USING C PROGRAMMING

OBJECTIVES:

• To be able to follow the algorithm of Newton's Backward Interpolation method to generate backward difference table.

• To build some programming concepts by solving practical problems.

 TOOLS REQUIRED:

• Computer workstation

• Program software (as necessary)

 THEORY:

While interpolating intermediate value of dependent variable for equi-spaced data of independent variable, at the end of the table, Newton's Backward Interpolation formula is used. 

 ALGORITHM:

1. Start

2. Read the number of data n and the datas.

3. Set i=1

4. Set j=n-1

5. Calculate y [j][i]=y [j][i-1]-y [j-1][i-1]

6. J=j-1

7. Goto step 5 if j > i-1

8. Set i=i+1

9. Goto step 4 if i < n

10. Display the table 

11. Stop

C-PROGRAM:   

#include
#include
void main()
{
 float x[20], y[20][20];
 int i,j, n;
 clrscr();
 printf("Enter number of data?\n");
 scanf("%d", &n);
 printf("Enter data:\n");
 for(i = 0; i < n ; i++)
 {
  printf("x[%d]=", i);
  scanf("%f", &x[i]);
  printf("y[%d]=", i);
  scanf("%f", &y[i][0]);
 }
 /* Generating Backward Difference Table */
 for(i = 1; i < n; i++)
 {
  for(j = n-1; j > i-1; j--)
  {
   y[j][i] = y[j][i-1] - y[j-1][i-1];
  }
 }
 /* Displaying Forward Difference Table */
 printf("\nBACKWARD DIFFERENCE TABLE\n\n");
 for(i = 0; i < n; i++)
 {
  printf("%0.2f", x[i]);
  for(j = 0; j <= i ; j++)
  {
   printf("\t%0.2f", y[i][j]);
  }
  printf("\n");
 }
 getch(); 
}

OUTPUT:

Enter number of data?
4
Enter data:
x[0]=0
y[0]=1
x[1]=1
y[1]=2
x[2]=2
y[2]=1
x[3]=3
y[3]=10

BACKWARD DIFFERENCE TABLE

0.00    1.00
1.00    2.00    1.00
2.00    1.00    -1.00   -2.00
3.00    10.00   9.00    10.00   12.00

CONCLUSION:

Thus the Backward difference table was generated  by using C Programming language.