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67 lines
2.0 KiB
C++
67 lines
2.0 KiB
C++
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/*----- CALCULATION OF TRUNCATION ERROR OF SERIES APPROXIMATION -------*/
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/* EXPONENTIAL SERIES exp(x) IS USED HERE
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INPUTS : 1) The total number of terms to be computed
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in series starting from first term.
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2) The value of 'x' in exp(x).
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OUTPUTS : 1) Computed value of series approximation of exp(x).
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2) Actual value of exp(x) function.
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3) Absolute error between series approximation and
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actual value of exp(x) function. */
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/*------------------------------ PROGRAM --------------------------*/
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#include<stdio.h>
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#include<math.h>
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#include<stdlib.h>
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#include<conio.h>
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void main()
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{
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double fact ( int n); /* DECLARATION OF FACTORIAL FUNCTION */
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double x,sum,z,sum1;
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int n,i;
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clrscr();
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printf("\n\t\tCALCULATION OF TRUNCATION ERROR "
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"OF SERIES APPROXIMATION");
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printf("\n\nGive number of terms "
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"in series to be computed = ");
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scanf("%d",&n); /* NUMBER OF TERMS TO BE COMPUTED IN SERIES */
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n = n - 1; /* TERMS ARE COMPUTED FROM ZERO HENCE 'n-1' */
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printf("\nGive value of x = ");
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scanf("%lf",&x); /* VALUE OF 'x' */
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sum = 0;
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sum1 = 0;
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for(i = 0; i<=n; i++)
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{
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z = fact(i);
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sum = pow(x,(double)i)/z;
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sum1 = sum1 + sum;
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}
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printf("\nThe computed value of exp(x) "
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"function is = %1.15lf",sum1); /* COMPUTED VALUE */
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printf("\n\nThe actual value of exp(x) "
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"function is = %1.15lf",exp(x)); /* ACTUAL VALUE */
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printf("\n\nTruncation error in series "
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"approximation is = %1.15lf", exp(x)-sum1); /* ERROR */
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}
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/*------------- FUNCTION PROCEDURE TO CALCULATE FACTORIAL -------------*/
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double fact( int n)
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{
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double facto;
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facto = 1;
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if(n == 0) return( facto = 1);
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do
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{
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facto = facto * n;
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}
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while(n-- > 1);
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return(facto);
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}
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/*----------------------- END OF PROGRAM ----------------------------*/
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