Numerically Solving Partial Differential Equations



 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: beroza %! at !% scripps.edu
  Department of Molecular Biology       phone: 619-784-9957
  10550 N. Torrey Pines Rd. - TPC15     fax: 619-784-8896
  La Jolla, CA 92037                    URL: www.scripps.edu/~beroza
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