Program to find the solution of the equation using Runge-Kutta fourth order Method

#include<stdio.h>

#include<conio.h>

#include<math.h>

int main()

{

float x1,y1,x2,y2,xf,h,s,s1,s2,s3,s4;

//clrscr();

printf("enter the initial points :\n");

scanf("%f%f",&x1,&y1);

printf("enter the final points :\n");

scanf("%f",&xf);

printf("enter the step size :\n");

scanf("%f",&h);

//printline();

printf("X\t\tY\n");

//printline();

printf("%.2f\t\t%.2f\n",x1,y1);

while(x1<=xf)

{

  s1=1-(x1*x1*x1);

  x2=x1+(h/2);

  y2=y1+(s1*(h/2));

  s2=1-(x1*x1*x1);

  y2=y1+(s2*(h/2));

  s3=1-(x1*x1*x1);

  x2=x1+h;

  y2=y1+(s3*h);

  s4=1-(x1*x1*x1);

  s=(s1+2*s2+2*s3+s4)/6;

  y2=y1+h*s;

  x1=x2;

  y1=y2;

  printf("%.2f\t\t%.2f\n",x1,y1);

}

getch();}

Program to find the solution of the equation using Euler's Method

#include<stdio.h>

#include<conio.h>

#include<math.h>

int main()

{

float x1,y1,x2,y2,xf,h,s;

//clrscr();

printf("enter the initial points :\n");

scanf("%f%f",&x1,&y1);

printf("enter the final points :\n");

scanf("%f",&xf);

printf("enter the step size :\n");

scanf("%f",&h);

printf("X\t\tY\n");

while(x1<=xf)

{

  printf("%.2f\t\t%.2f\n",x1,y1);

  s=x1*y1;

  y2=y1+h*s;

  x2=x1+h;

  x1=x2;

  y1=y2;

}

getch();

}

NEWTON DIVIDED DIFFERENCE FORMULA

#include<stdio.h>

#include<conio.h>

#include<stdlib.h>

#include<math.h>

#define n 5

int main()

{

    float y[n],x[n],d[n-1],xa,u,sum=0,tnum,tden;

    int i,j,l,k,m;

   // clrscr();

    printf("enter the values of interpolation x points\n");

    for(i=1;i<=n;i++)

    scanf("%f",&x[i]);

    printf("enter the corresponding values of y\n");

    for(i=1;i<=n;i++)

    scanf("%f",&y[i]);

    printf("enter the value of x at which y(x) is needed\n");

    scanf("%f",&xa);

    if(fabs(xa-x[1])>fabs(xa-x[n]))

    {

       printf("this is not a suitable formula\n");

         return(1);

     }

     m=n-1;

     for(i=1;i<n;i++)

                d[i]=y[i+1]-y[i];

                 for(i=2;i<n;i++)

                 {

                  for(l=i;i>l;l--)

                  printf("\t");

                   for(j=i;j<n;j++)

                   {

                   k=m-j+i;

                   d[k]=d[k]-d[k-1];

                   }

                   }

                   u=((xa-x[1])/fabs(x[2]-x[1]));

                   sum=y[1];

                   tnum=u;

                   tden=1.0;

                   for(i=1;i<n;i++)

                   {

                   sum=sum+(tnum/tden)*d[i];

                   tnum=tnum*(u-1);

                   tden=tden*(i+1);

                   }

                   printf("the value of y is %f\n",sum);

                   getch();

 }

Program to solve interpolation formula using Lagrange interpolation method

Here is a C program to solve interpolation formula using Lagrange interpolation method.

 #include<stdio.h>  
 #include<conio.h>  
 int main()  
 {  
 int n,i,j;  
 float x1,x[10],f[10],sum=0,pf;  
 //clrscr();  
 printf("enter the order of polynomial :\n");  
 scanf("%d",&n);  
 printf("enter the value to be find :\n");  
 scanf("%f",&x1);  
 printf("enter values for xi & f(xi) :\n");  
 for(i=0;i<n;i++)  
 {  
  scanf("%f",&x[i]);  
  scanf("%f",&f[i]);  
 }  
 sum=0;  
 for(i=0;i<(n+1);i++)  
 {  
  pf=1;  
  for(j=0;j<(n+1);j++)  
  {  
   if(j!=i)  
    pf=pf*(x1-x[j])/(x[i]-x[j]);  
    }  
  sum=sum+f[i]*pf;  
 }  
 printf("f(%.2f)=%.2f\n",x1,sum);  
 getch();  
 }  

Program to solve simultaneous equation using by Gauss Seidal Method

#include<stdio.h>

#include<conio.h>

#include<math.h>

int main()

{

int n,i,j,k,maxit;

float a[10][10],e,big,sum,temp,x[10],relerr,prod=1,prod1=1;

//clrscr();

printf("enter the allowable error :");

scanf("%f",&e);

printf("\nenter the maximum number of iteration :");

scanf("%d",&maxit);

printf("\nenter the number of equations :");

scanf("%d",&n);

printf("\nenter the co-efficients of equations :\n");

for(i=1;i<=n;i++)

 for(j=1;j<=(n+1);j++)

  scanf("%f",&a[i][j]);

printf("\nentered co-efficient matrix is\n");

for(i=1;i<=n;i++)

{

 for(j=1;j<=(n+1);j++)

  printf("%.2f\t",a[i][j]);

 printf("\n");

}

for(i=1,j=n;i<=n;i++,j--)

{

  prod=prod*a[i][i];

  prod1=prod1*a[i][j];

}

if(fabs(prod) < fabs(prod1))

{

  printf("diagonal dominancy");

  getch();

  return(0);

}

else

for(i=1;i<+n;i++)

  x[i]=0;

//printline();

for(i=1;i<=n;i++)

  printf("X%d\t",i);

printf("\n");

//printline();

for(k=1;k<=maxit;k++)

{

  big=0;

  for(i=1;i<=n;i++)

  {

    sum=0;

    for(j=1;j<=n;j++)

    {

      if(i!=j)

                sum=sum+a[i][j]*x[j];

    }//end for j

    temp=(a[i][n+1]-sum)/a[i][i];

    relerr=fabs((x[i]-temp)/temp);

    if(relerr>big)

      big=relerr;

    x[i]=temp;

    printf("%.2f\t",x[i]);

  }//end for i

  printf("\n");

  if(big<=e)

  {

    printf("\nconverges to a solution in %dth iteration",k);

    printf("\nsolution vector is:\n");

    for(i=1;i<=n;i++)

      printf("x[%d]=%.2f\n",i,x[i]);

    getch();

    return(0);

  }

    }//end for k

  printf("dose not converge in %d iterations",maxit);

  getch();

}

Program to solve simultaneous equation using by Guess Jordan method

#include<stdio.h>

#include<conio.h>

#include<math.h>

int main()

{

int n,i,j,k;

float a[10][10],x[10],u;

//clrscr();

printf("enter the number of equations :");

scanf("%d",&n);

printf("\nenter the co-efficients of equations\n");

for(i=1;i<=n;i++)

 for(j=1;j<=(n+1);j++)

  scanf("%f",&a[i][j]);

printf("\nentered co-efficient matrix is\n");

for(i=1;i<=n;i++)

{

 for(j=1;j<=(n+1);j++)

  printf("%.2f\t",a[i][j]);

 printf("\n");

}

    //Diagonalisation Steps//

for(k=1;k<=n;k++)

  for(i=1;i<=n;i++)

  {

    if(i != k)

    {

      u=a[i][k]/a[k][k];

      for(j=1;j<=(n+1);j++)

      a[i][j]=a[i][j]-(u*a[k][j]);

    }

  }

  printf("\nDiagonalised matrix is\n");

  for(i=1;i<=n;i++)

  {

    for(j=1;j<=(n+1);j++)

      printf("%.2f\t",a[i][j]);

    printf("\n");

  }

     //End Diagonalisation Steps//

     //Forward Substitution Steps //

  x[n]=a[n][n+1]/a[n][n];

  for(i=1;i<=n;i++)

    x[i]=(a[i][n+1])/a[i][i];

  printf("\nsolution vector is\n");

  for(i=1;i<=n;i++)

    printf("x[%d]=%.2f\n",i,x[i]);

  getch();

}

Program to solve simultaneous equation using by Guess elimination method

#include<stdio.h>

#include<conio.h>

#include<math.h>

//#include<stdlib.h>

int main()

{

int n,i,j,m,k,p,q;

float e,a[10][10],x[10],temp,max,sum,u;

//clrscr();

printf("enter the number of equations :");

scanf("%d",&n);

printf("\nenter the co-efficients of equations\n");

for(i=1;i<=n;i++)

 for(j=1;j<=(n+1);j++)

  scanf("%f",&a[i][j]);

printf("\nenter the value of prescribed precision :");

scanf("%f",&e);

printf("\nentered co-efficient matrix is\n");

for(i=1;i<=n;i++)

{

 for(j=1;j<=(n+1);j++)

  printf("%.2f\t",a[i][j]);

 printf("\n");

}

    //Lower Triangularisation Steps//

for(k=1;k<=(n-1);k++)

   //Pivotal Condensation Steps//

{

  max=fabs(a[k][k]);

  p=k;

  for(m=(k+1);m<=n;m++)

    if(max < fabs(a[m][k]))

    {

      max=fabs(a[m][k]);

      p=m;

    }

  if(max <= e)

  {

    printf("\nill conditional equation\n");

    return(0);

  }

  if (p!=k)

    for(q=k;q<=(n+1);q++)

    {

      temp=a[p][q];

      a[p][q]=a[k][q];

      a[k][q]=temp;

    }

    //End of Pivoting Steps.

  for(i=(k+1);i<=n;i++)

  {

    u=a[i][k]/a[k][k];

    for(j=k;j<=(n+1);j++)

      a[i][j]=a[i][j]-(u*a[k][j]);

  }

}

  printf("\nLower Triangularised matrix is\n");

  for(i=1;i<=n;i++)

  {

    for(j=1;j<=(n+1);j++)

      printf("%.2f\t",a[i][j]);

    printf("\n");

  }

     //End Lower Triangularisation Steps//

     //Backward Substitution Steps //

  x[n]=a[n][n+1]/a[n][n];

  for(i=(n-1);i>=1;i--)

  {

    sum=0;

    for(j=i+1;j<=n;j++)

      sum=sum+a[i][j]*x[j];

    x[i]=(a[i][j]-sum)/a[i][i];

  }

  printf("\nsolution vector is\n");

  for(i=1;i<=n;i++)

    printf("x[%d]=%.2f\n",i,x[i]);

  getch();

}

Program to find the roots of a polynomial equation using newton raphson method

#include<stdio.h>

#include<conio.h>

#include<math.h>

#define f(x) x*x*x-5*x+3

#define df(x) 3*x*x-5

//int printline()

//{

//int i;

//for(i=1;i<=60;i++)

//printf("-");

//printf("\n");

//}

int main()

{

float x0,x1,y0,dy0,e,delta;

int i,n;

printf("enter the initial guess\n");

scanf("%f%f",&x0,&x1);

printf("enter the prescribed precision value\n");

scanf("%f",&e);

printf("enter the maximum number of iteration\n");

scanf("%d",&n);

printf("enter the minimum allowed value of slope\n");

scanf("%f",&delta);

//printline();

printf("iter\tX0\tF(X0)\tF'(x0)\tX1\n");

//printline();

for(i=1;i<=n;i++)

{

  y0 = f(x0);

  dy0= df(x0);

  if ((fabs(dy0)) < delta)

  {

    printf("slope is too small\n");

    return(0);

  }

  x1=x0-(y0/dy0);

  printf("  %d\t%.2f\t%.2f\t%.2f\t%.2f\n",i,x0,y0,dy0,x1);

  if ((fabs(x1-x0)/x1)<=e)

  {

    //printline();

    printf("converges to the root\n");

    printf("number of iteration is %d\n",i);

    printf("root is %.2f\n",x1);

    getch();

    return(0);

  }

  x0=x1;

}

//printline();

printf("does not converges to the root in %d iteration",n);

getch();

}

Program to find the roots of a polynomial equation using method of false position

#include<stdio.h>

#include<conio.h>

#include<math.h>

#define f(x) x*x*x-4*x+1

int main()

{

float x0,x1,e,y0,y1,x2,y2;

int i,n;

//clrscr();

printf("enter the initial guesses\n");

scanf("%f%f",&x0,&x1);

printf("enter the prescribed precision value\n");

scanf("%f",&e);

printf("enter the maximum number of iteration\n");

scanf("%d",&n);

y0=f(x0);

y1=f(x1);

if(y0*y1 > 0)

{

  printf("initial guesses are not suitable\n");

  return (0);

  //exit(0);

}

//printline();

printf("iter\tX0\tF(X0)\tX1\tF(X1)\tX2\tF(X2)\n");

//printline();

//for(i=1;i<=n;i++)

{

  x2=(x0*y1-x1*y0)/(y1-y0);

  y2=f(x2);

  printf("  %d\t%.2f\t%.2f\t%.2f\t%.2f\t%.2f\t%.2f\n",i,x0,y0,x1,y1,x2,y2);

  if ((fabs(y2))<=e)

  {

    //printline();

    printf("converges to the root\n");

    printf("number of iteration is %d\n",i);

    printf("root is %.2f\n",x2);

    getch();

    return (0);

    //exit(0);

  }

  if (y0*y2>0)

  {

    x0=x2;

    y0=y2;

  }

  else

  {

    x1=x2;

    y1=y2;

  }

}

//printline();

printf("does not converges to the root in %d iteration",n);

getch();

}

Program to find the roots of a polynomial equation using bisection method

#include<stdio.h>

#include<conio.h>

#include<math.h>

#define f(x) x*x*x-x-1

int main()

{

float x0,x1,e,y0,y1,x2,y2;

int i=0;

printf("enter the initial guesses\n");

scanf("%f%f",&x0,&x1);

printf("enter the prescribed precision value\n");

scanf("%f",&e);

y0=f(x0);

y1=f(x1);

if(y0*y1>0)

{

  printf("initial guesses are not suitable\n");

  return(0);

}

//printline();

printf("iter\tX0\tF(X0)\tX1\tF(X1)\tX2\tF(X2)\n");

//printline();

while (fabs((x1-x0)/x1)>=e)

{

  x2=(x0+x1)/2;

  y2=f(x2);

  i=i+1;

  printf("  %d\t%.2f\t%.2f\t%.2f\t%.2f\t%.2f\t%.2f\n",i,x0,y0,x1,y1,x2,y2);

  if(y0*y2>0)

  {

    x0=x2;

}

  else

  {

    x1=x2;

}

}

printf("converges to the root\n");

printf("number of iteration is %d\n",i);

printf("root is %.2f",x2);

getch();

}