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);
}
}
}
}
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;
}
}
}
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();
}
}
