Re: solution of PDE
- To: mathgroup at smc.vnet.net
- Subject: [mg40754] Re: [mg40710] solution of PDE
- From: sean kim <shawn_s_kim at yahoo.com>
- Date: Wed, 16 Apr 2003 01:36:47 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
cb.
seems to me there aren't that many pde related posts
in this group. this is the third pde post I have
seen(two on diffusion/heat equation, and this one on
wave equation) I myself work with pde's ( diffusion as
with the other two who have posted and having same
problems as the other two as well)
my first suggestion is a book by martha abell and
james braselton entitled " differential equations with
mathematica"
the authors discuss the use of mathematica for solving
wave equations as well as other pde's in numerous
ways. it appears that you are at purdue, if that's
the case, i'm sure they have a copy of the book in
your school library. I think you will benefit
tremendously from it.
to start you off though...
to get the analytical solution you have to change your
pde into two second order ode's using separation of
variable and fourier sine series.
also you need the initial conidtions as well as the
boundary conditions.
for the problem of simple wave eqn, uxx = utt,
copy and paste the following into your mathematica
notebook and evaluate. below is equivalent to 4 cell
expressions, but it uses symbols and they dont paste
well into ascii message forums. but if you copy and
paste them they paste in mathematica format. good
luck.
\!\(a\_n_ =
2\ \(\[Integral]\_0\%1
x\ \((1 - x)\)\ Sin[n \[Pi] x]
\[DifferentialD]x\)\)
\!\(\(u[x_,
t_] = \[Sum]\+\(n = 1\)\%10\( 8\ Cos[\((2 n -
1)\)\ \[Pi] t]\ \
Sin[\((2 n - 1)\)\ \[Pi] x]\)\/\(\((2 n - 1)\)\^3\
\[Pi]\^3\);\)\)
\!\(\(somegraphs =
Table[Plot[u[x, t], {x, 0, 1}, DisplayFunction
-> Identity,
PlotRange -> {\(-0.3\), 0.3},
Ticks -> {{0, 1}, {\(-0.3\), 0.3}}], {t, 0,
1, 1\/15}];\)\n
\(toshow = Partition[somegraphs, 4];\)\n
Show[GraphicsArray[toshow]]\)
Show[GraphicsArray[toshow]]
--- C B <cbhat at herald.cc.purdue.edu> wrote:
> I am trying to solve the following PDE
>
>
>
> PDE : (1-M^2)D[phi[x,y],x,x]+ D[phi[x,y],y,y] = 0
>
> BC1: Derivative[0,1][phi][x,(d/2)] = U k A Cos(kx)
> BC2: Derivative[0,1][phi][x,(-d/2)] = U k A Cos(kx)
>
> But I Am not being able to get mathematica to do it.
>
> I know that the analyitcal solution exists and can
> be found out by
> seperation of variables. How do I get that solution
> using mathematica?
>
>
>
>
>
=====
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