Find the root of the equation using the Bisection method by MistarAV
#include<stdio.h>
#include<conio.h>
#include<math.h>
/*
Defining equation to be solved.
Change this equation to solve another problem.
*/
#define f(x) cos(x) - x * exp(x)
void main()
{
float x0, x1, x2, f0, f1, f2, e;
int step = 1;
clrscr();
/* Inputs */
up:
printf("\nEnter two initial guesses:\n");
scanf("%f%f", &x0, &x1);
printf("Enter tolerable error:\n");
scanf("%f", &e);
/* Calculating Functional Value */
f0 = f(x0);
f1 = f(x1);/* Checking whether given guesses brackets the root or not. */
if( f0 * f1 > 0.0)
{
printf("Incorrect Initial Guesses.\n");
goto up;
}
/* Implementing Bisection Method */
printf("\nStep\t\tx0\t\tx1\t\tx2\t\tf(x2)\n");
do
{
x2 = (x0 + x1)/2;
f2 = f(x2);
printf("%d\t\t%f\t%f\t%f\t%f\n",step, x0, x1, x2, f2);
if( f0 * f2 < 0)
{
x1 = x2;
f1 = f2;
}
else
{
x0 = x2;
f0 = f2;
}
step = step + 1;
}while(fabs(f2)>e);
printf("\nRoot is: %f", x2);
getch();
}
Output
Enter two initial guesses:
0
1
Enter tolerable error:
0.0001
Step x0 x1 x2 f(x2)
1 0.000000 1.000000 0.500000 0.053222
2 0.500000 1.000000 0.750000 -0.856061
3 0.500000 0.750000 0.625000 -0.356691
4 0.500000 0.625000 0.562500 -0.141294
5 0.500000 0.562500 0.531250 -0.041512
6 0.500000 0.531250 0.515625 0.006475
7 0.515625 0.531250 0.523438 -0.017362
8 0.515625 0.523438 0.519531 -0.005404
9 0.515625 0.519531 0.517578 0.000545
10 0.517578 0.519531 0.518555 -0.00242711 0.517578 0.518555 0.518066 -0.000940
12 0.517578 0.518066 0.517822 -0.000197
13 0.517578 0.517822 0.517700 0.000174
14 0.517700 0.517822 0.517761 -0.000012
Root is: 0.517761
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