sci.math.num-analysis #35010 (8 + 353 more)                      (1)+-[1]
From: Jason W DeGraw <degraw@math.psu.edu>                          |-[1]--[1]
[1] Re: KdV equation solution by finite difference                  \-[1]
Date: Tue May 27 21:32:56 EDT 1997
Lines: 25

Chris Rehmann wrote:
> 
> Would someone please suggest a finite-difference method for solving
> the KdV equation numerically?
> 
>         du/dt - 6 u du/dx + d3u/dx3 = 0

As an undergrad I did a term project using the scheme from:

Zabusky, N. J. and Kruskal, M. D.  Interaction of ``Solitons'' in a
Collisionless Plasma and the Recurrence of Initial States,
Physical Review Letters, 1965, Volume 15, #6, pages 240-243.

It is a leapfrog scheme if I recall correctly (I used several
schemes/methods and compared them).  This one is the simplest that I
used.  I tried to get a compact scheme to work, but I never managed to
get it right.  There were some others schemes that I looked at, but I
don't have the references handy.
 
Hope this helps.


Jason DeGraw
degraw@math.psu.edu
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sci.math.num-analysis #35018 (7 + 353 more)                      (1)+-(1)
From: markw@scs.leeds.ac.uk (M A Walkley)                           |-[1]--[1]
[1] Re: KdV equation solution by finite difference                  \-[1]
Date: Wed May 28 05:03:00 EDT 1997
Lines: 61

Hi Chris.

 The following references may be useful.

 Mark.


@article{V,
  author  = {Vliegenthart, A.C.},
  title   = {On Finite-Difference Methods for the 
            {K}orteweg-de {V}ries Equation},
  pages   = {137-155},
  journal = {Journal of Engineering Mathematics},
  volume  = {5},
  number  = {2},
  year    = {1971}  }

@article{GM,
  author  = {Greig, I.S. and Morris, J.L.},
  title   = {A Hopscotch Method for the 
            {K}orteweg-de-{V}ries Equation},
  pages   = {64-80},
  journal = {Journal of Computational Physics},
  volume  = {20},
  year    = {1976}  }

This reference is for a finite element method but they derive the
associated finite difference scheme at a node.

@article{SC,
  author  = {Sanz-Serna, J.M. and Christie, I.},
  title   = {Petrov-{G}alerkin Methods for 
             Nonlinear Dispersive Waves},
  pages   = {94-102},
  journal = {Journal of Computational Physics},
  volume  = {39},
  year    = {1981} }

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sci.math.num-analysis #35027 (6 + 353 more)                      (1)+-(1)
From: Ron Hardin <rhh@research.att.com>                             |-(1)--[1]
[1] Re: KdV equation solution by finite difference                  \-[1]
Date: Wed May 28 12:32:29 EDT 1997

The KdV equation is made to order for the Split-Step Fourier method;
in fact was one of its first applications.
-- 
Ron Hardin
rhh@research.att.com

On the internet, nobody knows you're a jerk.
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sci.math.num-analysis #35093 (5 + 353 more)                      (1)+-(1)
From: Frank Puffer <puffer@apx00.physik.uni-frankfurt.de>           |-(1)--(1)
[1] Re: KdV equation solution by finite difference                  \-[1]
Date: Fri May 30 09:47:54 EDT 1997

I obtained an acceptable accuracy by using central differences for the
spatial derivatives and 4th order Runge-Kutta for integrating the
resulting system of ODEs. The time step has to be quite small however to
obtain stability.

Frank
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