Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2005
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2005

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Partial diff equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58538] Re: Partial diff equations
  • From: carlos at colorado.edu
  • Date: Wed, 6 Jul 2005 03:11:22 -0400 (EDT)
  • References: <dad7uf$3k$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

You are expecting too much.  At the moment (perhaps things will be
different in 2100) computer algebra systems can help humans do
mathematics as tools, but cannot carry out any deep developments on
their own.  Its the difference between (a+b)^2=a^2+2ab+b^2 and FLT.

PDEs is one area where only humans can go deep because there are no
general solution methods, only some generic rules (Greens functions,
domain of validity, etc). Few can be solved in closed form for
arbitrary boundary or initial conditions.  I noticed that your example
has no specified domain or BCs. It is a particular solution.

On the other hand, many ODE classes are amenable to general solution
procedures, e.g. using Laplace or Fourier transforms, so they can be
put in a rule database, just like integrals.


  • Prev by Date: Re: Function to handle array with variable _number_ of dimensions?
  • Next by Date: Re: Function to handle array with variable _number_ of dimensions?
  • Previous by thread: Re: Partial diff equations
  • Next by thread: How to simulate random samples from crooked coin toss?