Subject: Numerically Solving Partial Differential Equations

From: Paul Beroza <[email-masked]>
Date: Mon, 12 May 1997 08:40:59 -0700 (PDT)

Gerald Loeffler wrote:

>
> The Delphi program by Barry Honig and co-workers solves the
> Poisson-Boltzmann equation (a partial differential equation in
> 3D-space)  by using a FINITE DIFFERENCE method.
> 
> I allways thought (without having considerable education in that field)
> that such equations are best and quite easily solved by FINITE ELEMENT
> methods.
> 
> Hence I wonder if someone could recommend a good, famous, concise book
> that deals with the general issue of how to numerically solve partial
> differential equations so that I better understand the rational behind
> Delphi's implementation.
>

Finite element methods will also work to solve the
Poisson-Boltzmann equation.  You (that's Tony You, not you personally)
and Harvey (and probably others) did this a few years back.  My 
understanding is that for large systems, like proteins, the number 
of elements required becomes quite large, and you can run out of memory.

Finite element, finite difference, and boundary element methods
can all be used to solve the Poisson-Boltzmann equation. I would
recommend "Numerical Recipes" as a good introduction to numerical
methods to solve partial differential equations.

Paul
  
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 Paul Beroza 
 The Scripps Research Institute        email: [email-masked]  
 Department of Molecular Biology       phone: 619-784-9957   
 10550 N. Torrey Pines Rd. - TPC15     fax: 619-784-8896   
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