SOME IMPORTANT NUMERICAL METHODS CODE IN JAVA

Bisection Method Code in Java:

class Processor

{

double method(double x)

 {

   double result=((x*x)-(5*x)+4);

   return result;

 }

 double error(double x1,double x2)

 {

  double result=(((x2-x1)/x2)*100);

   double error= Math.abs(result);

   return error;

   }

  double middle(double a,double b )

   {  

  double mid=((a+b)/2);

   return mid;

  }

}

 class bisectionmethod

{

 public static void main(String args[])

 {   

  Processor  p=new Processor();  

  double Xr_old=2;

   double Xu_old=8;

   double x1=Xr_old;

   double x2=Xu_old;

   double f1=p.method(x1);

  System.out.println("Function for Lower Limit :"+f1);

  double f2=p.method(x2);

  System.out.println("Function for Lower Limit :"+f2);

  System.out.println("\n");

  if(f1*f2==0)

  {

  if(f1==0)

  System.out.println("Root is :"+x1);

  else

  System.out.println("Root is :"+x2);

  }

 else if(f1*f2<0)  

 {

 for(int i=0;i<4;i++)

 {   

 System.out.println("Lower limit is :"+x1);

 System.out.println("Upper limit is :"+x2);

 f1=p.method(x1);

 f2=p.method(x2);

 System.out.println("f1="+f1+"\nf2="+f2);

 double Xr_new=p.middle(x1, x2);

 System.out.println("The root="+Xr_new);

 x2=Xr_new;

 double error=p.error(Xr_old,Xr_new);

 System.out.println("Error is :"+error);

 }

 }

  else if(f1*f2>0)  

 {

 for(int i=0;i<4;i++)

 {   

 System.out.println("Lower limit is :"+x1);

 System.out.println("Upper limit is :"+x2);

 f1=p.method(x1);

 f2=p.method(x2);

 System.out.println("f1="+f1+"\nf2="+f2);

 double Xr_new=p.middle(x1, x2);

 System.out.println("The root="+Xr_new);

 x1=Xr_new;

 double error=p.error(Xr_old,Xr_new);

 System.out.println("Error is :"+error);

 System.out.println("Xr is :"+Xr_new);

 double fr=p.method(Xr_new);

 System.out.println("fr:"+fr);

 }

  }

 }

 }

False Position  Method Code in Java:

class method

{

    double equation(double x)

    {

        double equ=x*x-x-2;

        return equ;

    }

 }

 class falsepositionmethod

{

 public static void main(String args[])

  { 

     method m= new method();

     double x1=1;

     double x2=3;

     for(int i=0;i<3;i++)

     {

     double fx1=m.equation(x1);

     double fx2=m.equation(x2);

    System.out.println("f(x1)="+fx1);

    System.out.println("f(x2)="+fx2);

     double x0=(x1)-((fx1)*((x2-x1)/fx2-fx1));

    System.out.println("X0="+x0);

    double fx=m.equation(x0);

    double f=(fx*fx1);

    System.out.println("ITERATION="+f);

    x1=x0;

     }

 }

}

Gauss Elimination Method Code in Java:

public class gausselemination

{

public static void main(String args[])

{

double c,u;

double a[][]=new double[4][4];

double b[]=new double[4];

double s[][]=new double[4][4];

double n[][]=new double[4][4];

double d[]=new double[4];

double m[]=new double[4];

a[1][1]=2;            a[1][2]=1;            a[1][3]=1;            b[1]=5;

a[2][1]=3;            a[2][2]=5;            a[2][3]=2;            b[2]=15;

a[3][1]=2;            a[3][2]=1;            a[3][3]=4;            b[3]=8;

c=a[1][1];

for(int i=1;i<3;i++)

               {

if(a[i][1]<a[i+1][1])

                                             c=a[i+1][1];

                              }

               }

               int p=1;

                              u=0;

               for(int i=1;i<4;i++)

               {

                              if(c==a[i][1])

                              {

                                             p=i;

                                             d[1]=a[p][1];      d[2]=a[p][2];      d[3]=a[p][3];      u=b[p];

                                             break;

                              }

               }

               if(p!=1)

               {

                              for(int i=1;i<4;i++)

               {

                                             if(p==i)

                                             {

                                                            for(int j=1;j<4;j++)

                                                                           a[p][j]=a[1][j];

                                             b[p]=b[1];

                                             break;

                                             }

                              }

                              a[1][1]=d[1];      a[1][2]=d[2];      a[1][3]=d[3];      b[1]=u;

               }

               System.out.println();

               for(int i=1;i<4;i++)

               {

                              for(int j=1;j<4;j++)

                              {

                                             System.out.print("               a["+i);System.out.print("]["+j);System.out.print("]="+a[i][j]);

                              }             System.out.print("               b["+i);System.out.print("]="+b[i]);System.out.println();

               }

               double a220,a230,a320,a330,a3300,x3,x2,x1,b20,b30,b300;

               a220=(a[1][2]*a[2][1]/a[1][1])-a[2][2];

               a230=(a[1][3]*a[2][1]/a[1][1])-a[2][3];

               b20=(b[1]*a[2][1]/a[1][1])-b[2];

               a320=(a[1][2]*a[3][1]/a[1][1])-a[3][2];

               a330=(a[1][3]*a[3][1]/a[1][1])-a[3][3];

               b30=(b[1]*a[3][1]/a[1][1])-b[3];

               a3300=(a230*a320/a220)-a330;

               b300=(b20*a320/a220)-b30;

               x3=b300/a3300;

               x2=(b20-(a230*x3))/a220;

               x1=(b[1]-a[1][2]*x2-a[1][3]*x3)/a[1][1];

              System.out.println();

               System.out.println("         X1== "+x1);       System.out.println();

               System.out.println("         X2== "+x2);       System.out.println();

               System.out.println("         X3== "+x3);       System.out.println();

}

}