*To*: mathgroup@smc.vnet.net*Subject*: [mg10818] Re: PDEs & Mathematica.*From*: Julian Stoev <stoev@SPAM-RE-MO-VER-usa.net>*Date*: Tue, 10 Feb 1998 21:01:33 -0500*Organization*: Seoul National University, Republic of Korea*References*: <199801270810.DAA01319@smc.vnet.net.> <6atasu$jlr$14@dragonfly.wolfram.com> <6ba9f1$bba@smc.vnet.net>

On 4 Feb 1998, Lars Hohmuth wrote: |Actually, both DSolve and NDSolve have routines for handling certain |classes of partial differential equations. More specifically, DSolve |uses separation of variables and symmetry reduction, while NDSolve uses |the method of lines for 1+1 dimensional PDEs. |You usually specify initial conditions exactly like in the ODE case, but |keep in mind that solving PDEs is a much harder problem than ODEs. For |example, partial differential equation may not have a general solution. |SO it would be helpful to know exactly which equations you are trying |to solve. |Here is an example from the online documentation. It finds a numerical |solution to the wave equation with the initial condition |y[x,0]=Exp[-x^2]. The result is a two-dimensional interpolation |function. |In[1]:NDSolve[{D[y[x, t], t, t] = D[y[x, t], x, x], | y[x, 0] = Exp[-x^2], Derivative[0,1][y][x, 0] = 0, | y[-5, t] = y[5, t]}, y, {x, -5, 5}, {t, 0, 5}] Out[1]{{y\[Rule]InterpolatingFunction[{{-5,5.},{0.,5.}},"<>"]}} |If general solutions don't exist, the standard package |Calculus`DSolveIntegrals` can be used to find complete integrals of the |PDE. Additionally, there are a couple of packages for calculating Lie |and Lie-Backlund symmetries available from www.mathsource.com. | |There are a number of books about solving differential equations with |Mathematica, take a look at |http://store.wolfram.com/catalog/books/de.html . |Some more information is available in sections 3.5.10 and 3.9.7 of the |Mathematica Book. |Lars Hohmuth |Wolfram Research, Inc. Hi! Since the question is about PDE and you seem to respond on this kind of messages from Wolfram Res., I would like to ask a question. It is not a secret, that many CAS can handle systems of PDE. I found good links about this on http://www.can.nl/Systems_and_Packages/Per_Purpose/Special/index.html#diffeqns It seems, that Mathematica is far behind others in this field :-(. Can you give some hints (if not secret) in which directions Mathematica may develop in near future. This may be very important for the users. And a question to others. I was not able to find package for Mathematica doing something more, then Lie-Backlund for general PDEs. Are there some other tools simillar in functionality to DSolve working on systems of PDE (may be linear or other special forms)? I am not a matematician, I am engineer. I need a tool which I would be able to use after reading may be 1 book, but 3 books in pure heavy mathematics is too much time for me. Thank you! -------------------------------------------------------------------------- Julian Stoev <j.h.stoev@ieee.org> - Ph. D. Student Intelligent Information Processing Lab. - Seoul National University, Korea Office: 872-7283, Home: 880-4215 - http://poboxes.com/stoev !!!!! Use REPLY-TO: or remove "SPAMREMOVER" in my address