This is a sample code for integrating Ito stochastic differential equations
with fixed step sizes, along with support routines and a sample driver.
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 2.0.4 of this integrator.


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The contents of this directory are:

README: this file

sderk90.f90: the file containing the integrator module

sdesample.f90: a sample driver for sderk90.f90 to integrate a problem 
               with a known analytic solution

sderk_support.f90: sample support module for sderk90.f90, implementing
                   the sample problem of test1.f90

utilities.f90: contains a routine used by test1.f to parse a command-line
               argument

runscript: shell script to run sdesample.f90 for a number of different 
           internal step sizes, dumping the results to a series of files
           along with the analytic solution

testscript.m: a script that runs in MATLAB or Octave to take the
              results generated by ruscript, calculate the global
              errors for the integration for different step sizes,
              plot them, and fit the global errors to empirically
              determine the global convergence order of the integration

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

See the individual files for further documentation.

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To modify this code to solve other problems, you will want to concentrate
on 'sdesample.f90' and 'sderk_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 code
implementing several stochastic Runge-Kutta formulae.
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,
but no such code exists for SDEs.

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To summarize: to compile, run, and test the example code, you might
do something like:

> tar xvzf sdesample.tgz
> cd sdesample
> make

Now you can try out the code, e.g.,

> sdesample 1

will run the code for a particular (fixed) step size, and 

> sdesample 2

will run the code with half that step size, but on the same Wiener path.
Note that this is not trivial, since to run with half the step size,
the Wiener path must be "refined" in a way that is consistent with the
original approximation.

To run the code for many step sizes automatically, try this:

> ./runscript

and then from within Octave, issue the command 'testscript'.
This will make a plot of the error of the numerical solution
as a function of the step size, and fit the result.
The answer should be around 1.5, since the integrator is
configured to use an order 1.5 method.