
IMPORTANT: To take advantage of this software (DEQ), you need the following
on your UNIX system: 

 (1) gnuplot OR grtool:
     
     gnuplot - information on how to obtain GNU software is located in
     the Simulation Digest tools directory.

     grtool - an interactive graphics plotting package for all plotting
     functions. grtool is in the simulation tools library at the University
     of Florida, and can be freely FTP'd. Follow the instructions by
     looking at the beginning of each Simulation Digest Issue
     (comp.simulation). If you want to avoid grtool, you can simply use
     your favorite graph plotting program. On UNIX systems you can get
     CRT plots by doing the following: %cat points | graph | plot -Tcrtplot.

 (2) gcc - one of the primary source routines is written in ANSI C. The
     c compiler 'gcc' is available freely from the Gnu Free Software 
     Foundation. See the file 'gnu.software.Z' also in the UF simulation
     library. This will give you information on how to get 'gcc'.

To make DEQ, do a 'make all'. Then you can run 'deq' from the
UNIX command line as follows:

%deq

You have the choice of entering one of two types of systems. Either

  (1) a single equation with high order terms (derivatives). Note
      that the system may be homogeneous or non-homogeneous, and that
      the left hand side of the equation must be the higher order
      term. Note the following notation: use x[1] for the first derivative
      of x with respect to time (i.e. x' or dx/dt), x[2] is the second
      derivative, and so on. x[0] is simply x.

  (2) a set of first order equations for an 'n'-dimensional system.
      You will be prompted for each equation in turn. Here x[1] means
      the first state variable. x[2] means the second state variable,
      and so on.


EXAMPLE 1
---------

An Example of a single equation is to enter:

  x[2] = -16*x[0] + 10*cos(3.7*t)

Note that this equation is x'' = -16x + 10cos(3.7t) using standard
notation. Try plotting this over time (always denoted as 't') by 
specifying 't' as the x-axis variable, and x[0] as the y axis 
variable to be plotted by grtool.

EXAMPLE 2
---------

An Example of the Lorenz System (Phase Plot) is to enter (note: left
hand sides of equations are prompted by DEQ):

  x[1]' = 10*(-x[1] + x[2])
  x[2]' = 28*x[1] - x[2] - x[1]*x[3]
  x[3]' = -2.666*x[3] + x[1]*x[2]

Try plotting x[1] vs. x[2] when prompted for this information.

------------------------------------------------------------------------
DEQ is composed of the following files:

Permanent files:

	deq.1   	the document describing this project.  To view,
			type  nroff -man deq.1 | more

	deq     	the batch file used to run DEQ.

	order1.c	the program which prompts the user for the
			equation(s) and any necessary info. Then
			transfers this info into a suitable format for
			the code generator.  

			NOTE: this code is in ANSI C.  To compile,
			type   gcc order1.c -o order1

	contsim.c	the program which converts the system of
			1st-order differential equations into an
			equivalent c program.  The integration method
			used is fourth-order Runge-Kutta. To compile,
			type  cc contsim.c -lm -o contsim

Temporary files:

	dump.in		the file containing a system of 1st-order 
			equations created by order1 and used by
			contsim.

	dump.c		the c source file created by contsim which,
			when run, creates dump.plot.  To compile,
			type   cc dump.c -lm -o dump

	dump		the executable file.

	dump.plot	the raw data created by dump which is used
			by grtool.

	



			
			


