*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