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: <email@example.com>
- 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.