1. Write a program to find the root of non-linear equation using Bisection method.

//Bisection Method
#include<stdio.h>
#include<conio.h>
#include<math.h>
#define MAX 20
#define E 0.00001
#define f(x) (x*x-4*x-10)
int main()
{   int count=0;
    float x1,x2,x0;
    printf("Enter the inital guess values x1 and x2\n");
    scanf("%f%f",&x1,&x2);
    if(f(x1)*f(x2)>0)
        printf("The guess values don\'t bracket root. Change the guess values.");
    else
    {   begin:
        x0=(x1+x2)/2;
        if(fabs(f(x0))<E)
        {
            printf("\nThe root is %f",x0);
            printf("\nNo. of iterations is %d",count);
        }
        else{
            if(f(x0)>0){
            x2=x0;
            count++;}
            else if(f(x0)<0){
            x1=x0;
            count++;}
            if (count<MAX)goto begin;
            else printf("\nThe process doesn\'t converge.");
        }
    }
    return 0;
}

Output:
 

2. Write a program to find the root of non-linear equation using Newton Raphson method.

//Newton Raphson Method
#include<stdio.h>
#include<conio.h>
#include<math.h>
#define MAX 20
#define E 0.0001
#define f(x) (exp(x)-x-2)
#define f1(x) (exp(x)-1)
int main()
{   int count=1;
    float x0,x1;
    printf("Enter the initial guess value. ");
    scanf("%f",&x0);
    if(f1(x0)==0)
        printf("Derivative is zero at guess value.");
    else
    {   begin:
        x1=x0-(f(x0)/f1(x0));
        if(fabs((x1-x0)/x1)<E)
        {
            printf("The root is %f",x1);
            printf("\nNo. of iterations is %d",count);
        }
        else
        {
            x0=x1;
            count++;
            if(count<MAX) goto begin;
            else
                printf("The process doesn\'t converge.");
        }
    }
    return 0;
}

Output:

 



3. Write a program to find the root of non-linear equation using Secant method.

//Secant Method
#include<stdio.h>
#include<conio.h>
#include<math.h>
#define MAX 20
#define E 0.0001
#define f(x) (exp(x)-x-2)
int main()
{   int count=1;
    float x1,x2,x3,f1,f2;
    printf("Enter two initial guess values. ");
    scanf("%f%f",&x1,&x2);
        begin:
        f1=f(x1),f2=f(x2);
        x3=x2-f2*(x2-x1)/(f2-f1);
        if(fabs((x3-x2)/x3)<E)
        {
            printf("The root is %f",x3);
            printf("\nNo. of iterations is %d",count);
        }
        else
        {
            x1=x2;
            f1=f2;
            x2=x3;
            count++;
            if(count<MAX) goto begin;
            else
                printf("The process doesn\'t converge.");
        }
    return 0;
}

Output:

 





4. Write a program to find the root of the non-linear equation using Fixed Point method.

//Fixed point method
#include<stdio.h>
#include<conio.h>
#include<math.h>
#define MAX 20
#define E 0.0001
#define g(x) (exp(x)-2) //exp(x)-x-2=0, x=exp(x)-2

int main()
{   int count=1;
    float x0,x1,error;
    printf("Enter the initial guess value. ");
    scanf("%f",&x0);
    begin:
        x1=g(x0), error=x1-x0;
        if(fabs(error)<E)
        {
            printf("The root is %f",x1);
            printf("\nNo. of iterations is %d",count);
        }
        else
        {
            x0=x1;
            count++;
            if(count<MAX) goto begin;
            else
                printf("The process doesn\'t converge.");
        }
    return 0;
}

Output: