// RK4th.java  basic step code
//  RUNGE-KUTTA 4th order step wise integration of
//  ordinary differential equation, given  f1(x,y) = dy/dx f(x,y)
//  and yStart at xStart,  find value  of f(x,y) at  x=xEnd

public class RK4th
{
  public RK4th() // constructor
  {
    double k1,k2,k3,k4;
    double x,y;
    double xStart, yStart, xEnd, yEnd, h;
    System.out.println("RK4th.java running");
    System.out.println("f(x,y)=(x-1)(x-2)(x-3)(x-4)");
    System.out.println("RK4th, enter xStart, yStart, xEnd, h");
    xStart=0.0;
    yStart=24.0;
    xEnd=5.0;
    yEnd=0.0;
    h=0.25; // power of 2 needed for near exact solution
    System.out.println("xStart= "+xStart);
    System.out.println("yStart= "+yStart);
    System.out.println("xEnd= "+xEnd);
    System.out.println("step size h= "+h);

    // set initial conditions
    x=xStart;
    y=yStart;
    while(x<xEnd)  // basic iteration, x incremented by step size h
    {
      k1=h*F1(x,y);
      k2=h*F1(x+h/2,y+k1/2);
      k3=h*F1(x+h/2,y+k2/2);
      k4=h*F1(x+h,y+k3);
      y=y+(k1+2*k2+2*k3+k4)/6; // 4th order estimate of y
      x=x+h;
      System.out.println("x="+x+"    y="+y);;
    }
    xEnd=x;
    yEnd=y;
    System.out.println("yEnd= "+yEnd+"  at xEnd="+x);
    System.out.println("y=0 expected at x=1,2,3,4");
    System.out.println("yEnd expected to be 24 at xEnd=5");
  }

  static double F1(double x, double y)
  {
    // derivitive of (x-1)(x-2)(x-3)(x-4)
    return 4.0*x*x*x - 30.0*x*x + 70.0*x - 50.0;
  }

  public static void main (String[] args)
  {
    new RK4th();
  }
} // end RH4th.java