Re: Re: solution of PDE
- To: mathgroup at smc.vnet.net
- Subject: [mg40791] Re: [mg40754] Re: [mg40710] solution of PDE
- From: Ferdinand <ferdinand.cap at eunet.at>
- Date: Thu, 17 Apr 2003 03:36:49 -0400 (EDT)
- References: <200304160536.BAA20216@smc.vnet.net>
- Reply-to: ferdinand.cap at eunet.at
- Sender: owner-wri-mathgroup at wolfram.com
you can find solutions of all 3 pde in my book :
Mathematical Methods in Physics and Engineering with
Mathematica,crcpress cjapman and hall, ISBN 1584884029
sean kim wrote:
> 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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- References:
- Re: solution of PDE
- From: sean kim <shawn_s_kim@yahoo.com>
- Re: solution of PDE