This is a sample code for integrating ordinary differential equations
using Adams-Bashforth formulae with adaptive step size and order.
All compilable code here is written in Fortran 90.

For assistance with running this code, contact the author, Daniel Steck,
at <dan at steck dot us>. 

This code is provided as-is, without warranty; you should thoroughly
test it before trusting it.  This code is free for non-commercial use.

This is version 1.0 of this integrator.


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The contents of this directory are:

README: this file

odeab90.f90: the file containing the integrator module

hosc.f90: a sample driver for odeab90.f90 to integrate a problem with a
          known analytic solution

globals.f90: defines global variables to be shared by multiple routines

odeab_support.f90: integrator support module, defining the equations of
                   motion for the problem, and interface stuff for odeab90.

utilities.f90: general-use utilities (hosc uses 's2r' to convert strings
               to real numbers)

Makefile: makefile for test1.f90, this tells the 'make' utility what to do


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To modify this code to solve other problems, you will want to concentrate
on 'hosc.f90' and 'odeab_support.f90'.  Read the extensive comments in
the source files to see what is going on.

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NOTE: this integrator is written by me and has not been tested by a
large user community for many years.  It is a sophisticated Adams-
Bashforth code with adaptive step size and adaptive integration order.
It should be high-quality and efficient, but there is always the
possiblity for finding a bug. 

Normally, I would recommend a production-quality integrator such
as ODEPACK, but I am building this example around this integrator
so you can have a portable, self-contained code.  This is particularly
important in this course since we don't have a specific "home" cluster.

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To try this out: download the source tarball, by using "download as"
in your browser or by using wget:

wget <url>

where <url> is the location of the source tarball odesample.tgz,
something like

  wget atomoptics.uoregon.edu/~dsteck/teaching/07spring/phys686/odesample.tgz

Now unpack it:

  tar xvzf odesample.tgz

Enter the unpacked directory:

  cd odesample

Build the source:

  make

Try running it:

  hosc

You should have gotten usage info.  Try a simulation:

  hosc 1 5 0.01 10

(What do the numbers mean?  Look at the usage info!)
You should have gotten a bunch of output, and some run-time diagnostics.
Do it again, but save the data to the file 'out.txt':

  hosc 1 5 0.01 10 > out.txt

Now plot it in gnuplot.  Make sure X Windows is running, then type

  gnuplot

Inside gnuplot, try this:

  plot 'out.txt' using 1:2 with lines

You should get a plot of the integrator solution.  Compare it to the
analytic solution by doing this:

  plot 'out.txt' using 1:2 with lines, 'out.txt' using 1:3 with lines

You shouldn't be able to see the difference, because the numerical
solution is very accurate.  How accurate?  Plot the difference:

  plot 'out.txt' using 1:($2-$3) with lines

Pretty accurate!  Now make this last plot pretty:

  set title 'My nice error plot (y0=1, omega=5)'
  set xlabel 'error'
  set ylabel 'time'
  replot

Suppose you want to print the plot out so you can frame it and hang it on
the wall for all your friends to see.  Let's make a postscript file
out of it, 'out.ps':

  set terminal postscript color
  set output 'out.ps'
  replot
  set terminal x11

The last bit prevents you from writing more to the file.  Now use gs
to view the file (gs out.ps), or make a pdf out of it, 'out.pdf':

  ps2pdf out.ps

On a mac, you can look at it in Preview.app:

  open out.pdf

To include this file in a LaTeX file (though you should really make
a nicer plot than this!), you could convert it to an .eps file:

  ps2eps -l out.ps

which gives you 'out.eps'.  This is assuming ps2eps is installed (it
is on my lab computers.)

By the way, if you want to delete all the object (.o) and executable
files after you're done, type

  make clean

This is also useful for force compilation over from scratch.

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