/*  
 *  - - - - - - - - 
 *   g a l _ r k f  
 *  - - - - - - - - 
 *  
 *  This routine is part of the General Astrodynamics Library  
 *
 *  Description:
 *
 *     This routine integrates an ordinary deferential equation 
 *     using the Runge-Kutte-Fehlberg method.
 *  
 *  Status: 
 *  
 *     Math special function.  
 *  
 *  Given:  
 *
 *     ystart          d[]          Starting y values
 *     nvar             i           Number of equations to integrate
 *     x1               d           Starting x value
 *     x2               d           Ending x value
 *     eps              d           Accuracy
 *     h1               d           First guess step-size
 *     hmin             d           Minimum step-size
 *     *derivs        func          User defined function for calculating the right hand side derivatives
 *     *rkfs          func          Required Runge-Kutte-Fehlberg stepper routine
 *     *derivsp         i           Pointer to parameters structure for derivs routine
 *
 *  Returned:  
 *  
 *     ystart          d[]          Ending y values
 *     gal_rkf          i           Status
 *                                    0 = Success
 *                                    1 = Failed to allocate workspace memory
 *                                    2 = Stepsize underflow
 *                                    3 = Maximum steps exceeded
 *                                    4 = Stepsize too small
 *  
 *  References:
 *
 *     NASA Technical Report TR R-352
 *     Some Experimental Results Concerning The Error Propagation in
 *     Runge-Kutte type integration formulas
 *     by Erwin Fehlberg
 *     October 1970
 *
 *  This revision:  
 * 
 *     2008 May 18
 *  
 *  Copyright (C) 2008 Paul C. L. Willmott. See notes at end. 
 *  
 *-----------------------------------------------------------------------  
 */  

#ifndef _GAL_RKF_H_  
#define _GAL_RKF_H_ 1  
  
#undef  __BEGIN_DECLS  
#undef  __END_DECLS  
#ifdef  __cplusplus  
#define __BEGIN_DECLS extern "C" {  
#define __END_DECLS }  
#else  
#define __BEGIN_DECLS /* empty */  
#define __END_DECLS   /* empty */  
#endif
  
__BEGIN_DECLS  

int gal_rkf
  (
    double ystart[],
    int nvar,
    double x1,
    double x2,
    double eps,
    double h1,
    double hmin,
    void ( *derivs ) ( double, double [], double [], int * ),
    int ( *rkfs ) ( double [], double [], int, double, double, double [], double [], void ( * ) ( double, double [], double [], int * ), int * ) ,
    int *derivsp
  ) ;
 
#endif /* !_GAL_RKF_H_ */ 

/*
 *  gal - General Astrodynamics Library  
 *  Copyright (C) 2008 Paul C. L. Willmott  
 *  
 *  This program is free software; you can redistribute it and/or modify  
 *  it under the terms of the GNU General Public License as published by  
 *  the Free Software Foundation; either version 2 of the License, or  
 *  (at your option) any later version.  
 *  
 *  This program is distributed in the hope that it will be useful,  
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of  
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the  
 *  GNU General Public License for more details.  
 *  
 *  You should have received a copy of the GNU General Public License along  
 *  with this program; if not, write to the Free Software Foundation, Inc.,  
 *  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.  
 *    
 *  Contact:  
 *    
 *  Paul Willmott  
 *  vp9mu@amsat.org  
 */  
  
