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# Re: PDEs & Mathematica.
*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!
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