Q1-write a program to find the root by using Bisection method.
#include<stdio.h>
#include<conio.h>
#include<math.h>
#define f(x) cos(x) - x * exp(x)
void main()
float x0, x1, x2, f0, f1, f2, e;
int step = 1;
up:
printf("\nEnter two initial guesses:\n");
scanf("%f%f", &x0, &x1);
printf("Enter tolerable error:\n");
scanf("%f", &e);
f0 = f(x0);
f1 = f(x1);
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;
Name-Aman Singh Dhek Section-F2 Roll no-10
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();
Name-Aman Singh Dhek Section-F2 Roll no-10
Output:
Name-Aman Singh Dhek Section-F2 Roll no-10
Q2--write a program to find the root by using fixed point interation
method.
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#define f(x) (pow(x, 3) - x - 1)
#define g(x) (cbrt(x + 1))
int main()
int count = 1, N;
float x0, x1, e;
printf("Enter initial guess: ");
scanf("%f", &x0);
printf("Enter tolerable error: ");
scanf("%f", &e);
printf("Enter maximum iterations: ");
scanf("%d", &N);
// printf("\nStep\tx0\t\tf(x0)\t\tx1\t\tf(x1)\n");
do
x1 = g(x0);
printf("%d\t%f\t%f\t%f\t%f\n", count, x0, f(x0), x1, f(x1));
Name-Aman Singh Dhek Section-F2 Roll no-10
count = count + 1;
if (count > N)
printf("Not Convergent.\n");
exit(0);
x0 = x1;
} while (fabs(f(x1)) > e);
printf("\nRoot is %f\n", x1);
return 0;
Name-Aman Singh Dhek Section-F2 Roll no-10
Output:
Name-Aman Singh Dhek Section-F2 Roll no-10
Q3--write a program to find the root by using Regula Falsi method.
#include<stdio.h>
#include<conio.h>
#include<math.h>
#define f(x) x*log10(x) - 1.2
int main()
float x0, x1, x2, f0, f1, f2, e;
int step = 1;
up:
printf("\nEnter two initial guesses:\n");
scanf("%f%f", &x0, &x1);
printf("Enter tolerable error:\n");
scanf("%f", &e);
f0 = f(x0);
f1 = f(x1);
if( f0*f1 > 0.0)
printf("Incorrect Initial Guesses.\n");
goto up;
/* Implementing Regula Falsi or False Position Method */
printf("\nStep\t\tx0\t\tx1\t\tx2\t\tf(x2)\n");
do
Name-Aman Singh Dhek Section-F2 Roll no-10
x2 = x0 - (x0-x1) * f0/(f0-f1);
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();
return 0;
Name-Aman Singh Dhek Section-F2 Roll no-10
Output:
Name-Aman Singh Dhek Section-F2 Roll no-10
Q4--write a program to find the root by using NEWTON RAMPSON
method.
#include<stdio.h>
#include<conio.h>
#include<math.h>
#include<stdlib.h>
#define f(x) 3*x - cos(x) -1
#define g(x) 3 + sin(x)
void main()
float x0, x1, f0, f1, g0, e;
int step = 1, N;
printf("\nEnter initial guess:\n");
scanf("%f", &x0);
printf("Enter tolerable error:\n");
scanf("%f", &e);
printf("Enter maximum iteration:\n");
scanf("%d", &N);
printf("\nStep\t\tx0\t\tf(x0)\t\tx1\t\tf(x1)\n");
do
g0 = g(x0);
f0 = f(x0);
if(g0 == 0.0)
printf("Mathematical Error.");
exit(0);
Name-Aman Singh Dhek Section-F2 Roll no-10
}
x1 = x0 - f0/g0;
printf("%d\t\t%f\t%f\t%f\t%f\n",step,x0,f0,x1,f1);
x0 = x1;
step = step+1;
if(step > N)
printf("Not Convergent.");
exit(0);
f1 = f(x1);
}while(fabs(f1)>e);
printf("\nRoot is: %f", x1);
getch();
Name-Aman Singh Dhek Section-F2 Roll no-10
Output:(3x-cos(x)-1
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Output: x-exp(x)
Name-Aman Singh Dhek Section-F2 Roll no-10
Output: x*x-30
Name-Aman Singh Dhek Section-F2 Roll no-10
Q5---write a program to find the root by using secant method.
#include<stdio.h>
#include<conio.h>
#include<math.h>
#include<stdlib.h>
#define f(x) x*x*x - 2*x - 5
void main()
float x0, x1, x2, f0, f1, f2, e;
int step = 1, N;
printf("\nEnter initial guesses:\n");
scanf("%f%f", &x0, &x1);
printf("Enter tolerable error:\n");
scanf("%f", &e);
printf("Enter maximum iteration:\n");
scanf("%d", &N);
/* Implementing Secant Method */
printf("\nStep\t\tx0\t\tx1\t\tx2\t\tf(x2)\n");
do
f0 = f(x0);
f1 = f(x1);
if(f0 == f1)
printf("Mathematical Error.");
exit(0);
Name-Aman Singh Dhek Section-F2 Roll no-10
}
x2 = x1 - (x1 - x0) * f1/(f1-f0);
f2 = f(x2);
printf("%d\t\t%f\t%f\t%f\t%f\n",step,x0,x1,x2, f2);
x0 = x1;
f0 = f1;
x1 = x2;
f1 = f2;
step = step + 1;
if(step > N)
printf("Not Convergent.");
exit(0);
}while(fabs(f2)>e);
printf("\nRoot is: %f", x2);
getch();
Name-Aman Singh Dhek Section-F2 Roll no-10
Output:
Name-Aman Singh Dhek Section-F2 Roll no-10
Q6---write a program to find the root by gauss elimination method.
#include<stdio.h>
#include<conio.h>
#include<math.h>
#include<stdlib.h>
#define SIZE 10
int main()
float a[SIZE][SIZE], x[SIZE], ratio;
int i,j,k,n;
printf("Enter number of unknowns: ");
scanf("%d", &n);
for(i=1;i<=n;i++)
for(j=1;j<=n+1;j++)
printf("a[%d][%d] = ",i,j);
scanf("%f", &a[i][j]);
for(i=1;i<=n-1;i++)
if(a[i][i] == 0.0)
printf("Mathematical Error!");
exit(0);
Name-Aman Singh Dhek Section-F2 Roll no-10
}
for(j=i+1;j<=n;j++)
ratio = a[j][i]/a[i][i];
for(k=1;k<=n+1;k++)
a[j][k] = a[j][k] - ratio*a[i][k];
x[n] = a[n][n+1]/a[n][n];
for(i=n-1;i>=1;i--)
x[i] = a[i][n+1];
for(j=i+1;j<=n;j++)
x[i] = x[i] - a[i][j]*x[j];
x[i] = x[i]/a[i][i];
/* Displaying Solution */
printf("\nSolution:\n");
for(i=1;i<=n;i++)
printf("x[%d] = %0.3f\n",i, x[i]);
return(0);
Name-Aman Singh Dhek Section-F2 Roll no-10
Output:
Name-Aman Singh Dhek Section-F2 Roll no-10
Q7---write a program to find the root by gauss jordan method.
#include<stdio.h>
#include<conio.h>
#include<math.h>
#define SIZE 10
int main()
float a[SIZE][SIZE], x[SIZE], ratio;
int i,j,k,n;
clrscr();
printf("Enter number of unknowns: ");
scanf("%d", &n);
/* 2. Reading Augmented Matrix */
printf("Enter coefficients of Augmented Matrix:\n");
for(i=1;i<=n;i++)
for(j=1;j<=n+1;j++)
printf("a[%d][%d] = ",i,j);
scanf("%f", &a[i][j]);
/* Applying Gauss Jordan Elimination */
for(i=1;i<=n;i++)
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{
if(a[i][i] == 0.0)
printf("Mathematical Error!");
exit(0);
for(j=1;j<=n;j++)
if(i!=j)
ratio = a[j][i]/a[i][i];
for(k=1;k<=n+1;k++)
a[j][k] = a[j][k] - ratio*a[i][k];
/* Obtaining Solution */
for(i=1;i<=n;i++)
x[i] = a[i][n+1]/a[i][i];
/* Displaying Solution */
printf("\nSolution:\n");
for(i=1;i<=n;i++)
printf("x[%d] = %0.3f\n",i, x[i];
Name-Aman Singh Dhek Section-F2 Roll no-10
Output:
Name-Aman Singh Dhek Section-F2 Roll no-10
