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Chapter:
1. 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:
Start
Read the number of data n and the datas.
Set i=1
Set j=n-1
Calculate y [j][i]=y [j][i-1]-y [j-1][i-1]
J=j-1
Goto step 5 if j > i-1
Set i=i+1
Goto step 4 if i < n
Display the table
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.
