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MathGroup Archive 1998

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Re: Re: PDEs & Mathematica.


  • To: mathgroup@smc.vnet.net
  • Subject: [mg10734] Re: [mg10700] Re: [mg10642] PDEs & Mathematica.
  • From: Richard Gass <gass@physics.uc.edu>
  • Date: Mon, 2 Feb 1998 00:44:27 -0500
  • References: <199801270810.DAA01319@smc.vnet.net.>

>William Golz wrote:
>>
>> The "online book" does not describe how to plug in initial and boundary
>> conditions for a PDE; and when I try to do it ODE style, which is
>> explained I get error messages. If anyone knows the proper syntax for
>> solving PDEs with boundary conditions, I would appreciate some advice.
>>
>> I would also appreciate any information on good books dealing with PDEs
>> and Mathematica.
>>
>> ____________
>> William Golz
>> Department of Civil & Environmental Engineering Louisiana State
>> University
>> Baton Rouge, Louisiana 70803
>>
>> E-mail: wgolz@unix1.sncc.lsu.edu
>> Phone:  (318)237-8353
>
Sean Ross wrote
>
>The DSolve and NDSolve do not contain routines for partial differential
>equations.  I am not aware of any other built-in functions that have
>routines for partial differential equations. --

 Actually NDSolve can solve 1+1 (one space and one time) dimensional
PDEs if they are Cauchy initial value problems. DSolve will solve so
PDEs although I have never gotten it to solve a PDE I cared about.
Examples of using NDSolve of PDEs and intial value problems can be
found in my book Mathematica for Scientists and Engineers , Prentice
Hall 1998. A short exsample is given below

S=Pi r^2;
r=(1/5)(1+Sin[1+x]^2);

FluidEquation=(1/S)D[S D[\[Psi][x,t],x],x]-(1/c^2)D[\[Psi][x,t],{t,2}]

Clear[c,\[Psi]]
c=342;
solution=NDSolve[{FluidEquation==0,\[Psi][x,0]==Exp[-(x)^2],
       
Derivative[0,1][\[Psi]][x,0]==100,\[Psi][-2Pi,t]==\[Psi][2Pi,t]},{
        \[Psi]},{x,-2Pi,2Pi},{t,0,2\[Pi]/342}][[1,1,2]]

P=D[solution[x,t],t]

DensityPlot[Evaluate[P],{x,-2Pi,2Pi},{t,0,2\[Pi]/342},PlotPoints->120,
  Mesh->False,ColorFunction->Hue,AxesLabel->{"x","t"},Axes->True,
  PlotLabel->"density plot of the  excess pressure"];

This example will take a fair bit of memory.

Richard Gass
Department of Physics
University of Cincinnati
Cincinnati, OH 45221
phone- 513-556-0519
E-Mail gass@physunc.uc.edu




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