! 	  From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
! 		by RH Landau, MJ Paez, and CC Bordeianu 
! 		Copyright Wiley - VCH, 2007.
! 		Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
! 		MJ Paez, Univ Antioquia, 2007; and CC Bordeianu, Univ Bucharest, 2007.
! 		Supported by the US National Science Foundation								
! 			
! 	 rk4.f90:	 4th order rk solution for harmonic oscillator			 
  
Program oscillator

	Implicit none
 ! n: number of equations, min/max in x, dist: length of x - steps
 ! y(1): initial position, y(2):initial velocity
	Real*8 :: dist, min1, max1, x, y(5)
	Integer :: n
	
	n = 2
	min1 = 0.0;  max1 = 10.0
	dist = 0.1
	y(1) = 1.0; 	y(2) = 0. 
	open(6, File = 'rk4.dat', Status = 'Unknown')
                                            ! Do n steps rk algorithm
	Do	x = min1, max1, dist
	  call rk4(x, dist, y, n)
		write (6, *) x, y(1)
	End Do
	close(6)
	Stop 'data saved in rk4.dat'
End Program oscillator                          ! End of main Program

subroutine rk4(x, xstep, y, n)                       ! rk4 subroutine
	Implicit none 
	Real*8 :: deriv, h, x, xstep, y(5) 
	Real*8, dimension(5) :: k1, k2, k3, k4, t1, t2, t3
	Integer :: i, n
	h = xstep/2.0
	Do	i = 1, n
	  k1(i) = xstep * deriv(x, y, i)
		t1(i) = y(i) + 0.5*k1(i)
	End Do
	Do	i = 1, n
	  k2(i) = xstep * deriv(x + h, t1, i)
		t2(i) = y(i) + 0.5*k2(i)
	End Do
	Do	i = 1, n
	  k3(i) = xstep * deriv(x + h, t2, i)
		t3(i) = y(i) + k3(i)
	End Do
	Do	i = 1, n
	  k4(i) = xstep * deriv(x + xstep, t3, i)
		y(i) = y(i) + (k1(i) + (2.*(k2(i) + k3(i))) + k4(i))/6.0
	End Do
	Return
End
                                       ! Function Returns derivatives
Function deriv(x, temp, i)
	Implicit none 
	Real*8 :: deriv, x, temp(2)
	Integer :: i 
	If (i == 1) deriv = temp(2)
	If (i == 2) deriv = - temp(1)
	Return
End