## Numerical Analysis : Runge Kutta Method

Runge Kutta method is a part of numerical analysis. Its an iterative method. To know more read :- CLICK

Java Code for Runga Kutta :

```import java.util.Scanner;

public class runge {

public static double f(double p,double q){

return (q/2+3*p);

}

public static void main(String[] args){

Scanner sc=new Scanner(System.in);

int n,choice,i;

double x0,y0,h,y1,x1,z0,sum,temp,k1,k2,k3,k4;

int ans;

System.out.println(" Enter  starting value of x and corr. value of y"+"\n");

x0=sc.nextDouble();

y0=sc.nextDouble();

System.out.println("Enter the value of x for which y is found"+"\n");

x1=sc.nextDouble();

System.out.println("Enter the step size"+"\n");

h=sc.nextDouble();

do{

k1=h*f(x0,y0);

k2=h*f((x0+h)/2,(y0+k1)/2);

k3=h*f((x0+h)/2,(y0+k2)/2);

k4=h*f((x0+h),(y0+k3));

System.out.println("The solution at " + x1 + "and" + y0 +"\n");

System.out.println("k1 "+ k1 +"\n");

System.out.println("k2 "+ k2 +"\n");

System.out.println("k3 "+ k3 +"\n");

System.out.println("k4 "+ k4 +"\n");

y1=(k1+2*k2+2*k3+k4)/6;

y1=y1+y0;

System.out.println(" Solution when h " + h + " is " + y1 +"\n");

System.out.println(" Goto next step???(Y=1/N=0)" +"\n");

ans=sc.nextInt();

if(ans==1){

x0=x0+h;

y0=y1;

x1=x0;

}

}while(ans==1);

}

}

```