Subject: Re: CCL:Gear method

From: [email-masked] (David C. Doherty)
Date: Wed, 10 May 1995 10:50:30 -0600

At 12:16 PM 5/10/95, Sergei Vyboishchikov wrote:
>A friend of mine looks for a Fortran source code for solving a
>system of stiff first-order differential equations implementing the
>Gear method. Any hints and advices would be appreciated.

Although this doesn't have anything to do with the
above request, I once saw Richard Gear in the movie
"Pretty Woman," and my company sells a "powerful-yet-
easy-to-use" program for Windoze which may do something
completely different than what you're looking for.

But what the heck, here comes the obligatory gratuitous
plug anyway:

<snip>

--

On the other hand, you may have some luck poking
around at netlib, for instance:

  http://www.netlib.org/ode/index.html
  ftp://ftp.netlib.org/ode/index

  http://www.netlib.org/odepack/index.html
  ftp://ftp.netlib.org/odepack/index

--

A snippet from the odepack description:

  1. LSODE (Livermore Solver for Ordinary Differential Equations) is the
     basic solver of the collection.  It solves stiff and nonstiff systems
     of the form dy/dt = f.  In the stiff case, it treats the Jacobian matrix
     df/dy as either a full or a banded matrix, and as either user-supplied
     or internally approximated by difference quotients.  It uses Adams methods
     (predictor-corrector) in the nonstiff case, and Backward Differentiation
     Formula (BDF) methods in the stiff case.  The linear systems that arise
     are solved by direct methods (LU factor/solve).  LSODE supersedes the older
     GEAR and GEARB packages, and reflects a complete redesign of the user
     interface and internal organization, with some algorithmic improvements.

  2. LSODES, written jointly with A. H. Sherman, solves systems dy/dt = f
     and in the stiff case treats the Jacobian matrix in general sparse
     form.  It determines the sparsity structure on its own (or optionally
     accepts this information from the user), and uses parts of the Yale Sparse
     Matrix Package (YSMP) to solve the linear systems that arise.
     LSODES supersedes, and improves upon, the older GEARS package.

---
David C. Doherty
Minnesota Supercomputer Center, Inc.
[email-masked]