------------>>>RK4<<<------------
                  Differential Equation Solver, Version 2.1
                       by Jorge Costa, November 26, 1995

Introduction:
------------

 RK4 solves differential equations using the fourth order Runge-Kutta method. 
Although it calculates N values of Y(T), the target solution is Y(b).
 Precisely, it solves Y(b) for a problem like:
                      /Y'(T,Y)=F(T,Y)
                      \Y(a)=Yi  and  a<=T<=b
given a, b, Yi, F(T,Y) and the number of interval steps, N.         

Installation note:
-----------------

 To successfully install RK4, just be sure to download the file using binary 
transfer. I recommend using X-modem protocol, for speed.

User instructions:
-----------------

 At start, input the requested data and wait a few seconds. Then, you shall
enter in a special environment which allows you to analyze the solution in 
detail:

 [PLOT]    - Draws a scatter-plot of the obtained data.
 [CHART]   - Enters in the MATRIX WRITER environment where you can manipulate
 intermediate results ( pick them to stack, not change them ).
 [EQN]     - Solved equation viewer ( press ON to exit ).
 [SAVE]    - Saves obtained data.
 [ABOUT]   - About the authors of RK4.
 [EXIT]    - Quit RK4.

 If you just want the value Y(b), don't worry: press [EXIT] and there it is
waiting for you in the stack!

Special notes to the user:
-------------------------

 During the writing of the code, I never forgot the actions that a new RK4 
user could take. So, don't worry if you make any mistakes during data input
because RK4 is completely BULLET PROOF!!
 I think this feature really took some extra bytes, but it surely provides 
more safety and trust to the user.  
 At last, the final environment lets you access to some useful routines and
obligates you to exit RK4 by pressing [EXIT] (so that there's no garbage in 
the VAR menu), because all non-menu keys have been disabled.

Bytes & Checksum : 2639.5  #21CBh ( #8651d )
(If you do 'RK4' RCL BYTES and you don't get these numbers, the file is
corrupted. Please e-mail me and I'll send you the latest version.)

IMPORTANT NOTE:
--------------

 The use of this software is not supported by ANY kind of guaranties related
to incidental or consequential damages suffered by users or hardware. 
 If the program is used, that means the user agrees with the rules and
distribution conditions mentioned in this document ( below ). The program has 
been tested in HP48 ROM versions J, P and R, which means that it must work in 
ALL HP48 calculators. If any kind of problems occur related to the use of RK4,
please report it to me by e-mail.
 
Acknowledgments: 
---------------

 This started from a one week holiday project that I really enjoyed to execute 
and that almost continuously drove my attention. Also, this is one of my first
ideas converted to System RPL, the internal language of the HP48. There is
one person who made things a lot easier to me and really encouraged me to
realize this project, he must be remembered: thanks Mario Fiadeiro!!
 Also, special thanks to:

- Mika Heiskanen, for JAZZ.LIB, HACK.LIB and for ENTRIES.SRT .
- Detlef Mueller, for the RPL48 toolkit .
- Jim Donnelly, for is book "An Introduction to System RPL and Assembly 
  Language Programming".

Distribution:
------------

 As a GIFTWARE release, the RK4V21.ZIP file can be freely copied, but with
the following conditions: 

1. It may not be modified without my permission.
2. Bugs, suggestions, improvements must be reported to my e-mail address.
3. If the user keeps it, he must send me ( at least ) a greeting card!
                                      

In the hope that the user enjoys it, I say good-bye and thanks for using it...

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   |      -Jorge Costa-   _Chemical Eng. Student & HP48 maniac_     |
   |                   < l38861@alfa.ist.utl.pt >                   |
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