!Runge-Kutta Method
		!Give the value of x0 and n here 
                !where x0 is initial value at time t=0 and n is number of iteration	
		!Time for which program runs is n*dt where dt=0.001 which can be changed 
		!in the program
		!Output is stored in fort.54 as time vesus x
	
	       ! Solution for this differentoal equation is
	       ! t=log(((1/sin(x0))+(cos(x0)/sin(x0)))/((1/sin(x))+(cos(x)/sin(x))))   
	       ! where log is to the base e (natural log)

		PROGRAM PROBLEM !2
		implicit real*8(a-h,o-z)
		pi=4d0*datan(1d0)

		x0=Pi/2d0
		dt=0.001d0
		n=10000
		WRITE(6,*)SIN(x0)
		DO i1=0,n-1
		rk1=SIN(x0)
		rk2=SIN(x0+0.5d0*dt*rk1)
		rk3=SIN(x0+0.5d0*dt*rk2)
		rk4=SIN(x0+dt*rk3)
		 x0new=x0+(dt/6d0)*(rk1+2d0*rk2+2d0*rk3+rk4)
		
		 WRITE(54,*)dt*DFLOAT(i1),x0 
		!x0new=x0+dt*SIN(x0)
		x0=x0new
		END DO
	      
		END