You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
75 lines
2.8 KiB
C++
75 lines
2.8 KiB
C++
|
|
|
|
/*------------ BISECTION METHOD TO FIND ROOT OF AN EQUATION ----------*/
|
|
|
|
/* THE EXPRESSION FOR AN EQUATION IS DEFINED IN function fx
|
|
YOU CAN WRITE DIFFERENT EQUATION IN function fx.
|
|
HERE,
|
|
f(x) = x*x*x - 1.8*x*x - 10*x - 17
|
|
|
|
INPUTS : 1) Initial interval [a,b] in which root is to
|
|
be found.
|
|
2) Permissible error in the root.
|
|
|
|
OUTPUTS : 1) Number of iterations for given interval and
|
|
permissible error.
|
|
3) Value of the root in given interval. */
|
|
|
|
/*------------------------------ PROGRAM --------------------------*/
|
|
|
|
#include<stdio.h>
|
|
#include<math.h>
|
|
#include<stdlib.h>
|
|
#include<conio.h>
|
|
|
|
void main()
|
|
{
|
|
double fx ( double x); /* DECLARATION OF FUNCTION */
|
|
double x,a,b,fa,fb,c,fc,err;
|
|
int n,i;
|
|
clrscr();
|
|
printf("\n BISECTION METHOD TO FIND ROOT OF AN EQUATION");
|
|
printf("\n\n f(x) = x*x*x - 1.8*x*x - 10*x - 17");
|
|
printf("\n\nEnter an interval [a,b] in "
|
|
"which root is to be found");
|
|
printf("\na = ");
|
|
scanf("%lf",&a); /* INTERVAL [a,b] IS TO BE ENTERED HERE */
|
|
printf("b = ");
|
|
scanf("%lf",&b);
|
|
printf("\nEnter the value of permissible error = ");
|
|
scanf("%lf",&err);
|
|
n = (log10(abs(b - a)) - log10( err ) )/log10(2);
|
|
/* CALCULATION OF STEPS 'n' */
|
|
n = n + 1; /* n SHOULD NOT BE A FRACTIONAL NUMBER; ADD '1' */
|
|
i = 0;
|
|
printf("\nNumber of iterations for this error bound are = %d",n);
|
|
printf("\n\npress any key for step by step display of intervals");
|
|
getch();
|
|
printf("\n\n RESULTS OF BISECTION METHOD\n");
|
|
while(n-- > 0)
|
|
{
|
|
fa = fx(a); /* CALCULATE f(x) AT x = a */
|
|
fb = fx(b); /* CALCULATE f(x) AT x = b */
|
|
c = (a + b)/2; /* CENTER OF THE INTERVAL */
|
|
fc = fx(c); /* CALCULATE f(x) AT x = c */
|
|
i++;
|
|
printf("\n\n%d a = %lf b = %lf c = %lf",i,a,b,c);
|
|
printf("\n f(a) = %lf f(b) = %lf f(c) = %lf",fa,fb,fc);
|
|
if( (fc*fa) < 0) b = c; /* IF f(c)f(a) < 0, NEW INTERVAL IS [a,c] */
|
|
if( (fc*fb) < 0) a = c; /* IF f(c)f(b) < 0, NEW INTERVAL IS [b,c] */
|
|
printf("\n interval : a = %lf b = %lf",a,b);
|
|
getch();
|
|
}
|
|
x = a + (b - a)/2; /* ROOT = a + half interval [a,b] */
|
|
printf("\nThe value of root is = %20.15lf",x); /* ROOT */
|
|
}
|
|
/*---------- FUNCTION PROCEDURE TO CALCULATE VALUE OF EQUATION --------*/
|
|
|
|
double fx ( double x)
|
|
{
|
|
double f;
|
|
f = x*x*x - 1.8*x*x - 10*x + 17; /* FUNCTION f(x) */
|
|
return(f);
|
|
}
|
|
/*------------------------ END OF PROGRAM -----------------------------*/
|