DEFINITION MODULE RKs;

   (* EXPORT QUALIFIED RK4, RKDumb; *)

   FROM NRVect IMPORT Vector;
   FROM NRMatr IMPORT Matrix;
   FROM NRMath IMPORT DerivFunction;

   PROCEDURE RK4(Y, DYDX: Vector;
                 x, h: REAL; 
                 derivs: DerivFunction; 
                 YOUT: Vector); 
   (*
     Given values for n variables Y[0, n-1] and their derivatives DYDX[0, n-1]
     known at x, use the fourth-order Runge-Kutta method to advance the 
     solution over an interval h and return the incremented variables as 
     YOUT[0, n-1], which need not be a distinct array from Y. The user supplies 
     the routine derivs(x,y,DYDX) which returns 
     derivatives DYDX at x.
   *)

   PROCEDURE RKDumb(VStart: Vector; 
                    x1, x2: REAL; 
                    nstep: INTEGER;
                    derivs: DerivFunction;
                    RKDumbX: Vector;
                    RKDumbY: Matrix); 
   (*
     Starting from initial values VSTART[0, n-1] for n functions
     known at x1, use fourth-order Runge-Kutta to advance nstep equal 
     increments to x2. Initial values and results of each step are stored 
     in the global variables RKDumbX[nstep+1], RKDumbY[N, (nstep+1)].
     The user-supplied routine derivs(x,V,DVDX) evaluates derivatives.
   *)

END RKs.