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Re: Newbe: Wave equation


  • To: mathgroup@smc.vnet.net
  • Subject: [mg12609] Re: Newbe: Wave equation
  • From: Bill Bertram <wkb@ansto.gov.au>
  • Date: Mon, 25 May 1998 14:25:19 -0400
  • Organization: ANSTO
  • References: <6k7e0q$1me@smc.vnet.net>

Michal Morawski wrote:
> 
> Hi,
> 
> I got the trial version of Mathematica 3.0. One of the first problems I
> want to solve was (is) the wave equation:
> 
> I wrote the following lines:
> c[x_] := if[ (x > 0.5) && ( x < 0.75), 3, 2]; R = 2+0.5 I;
> solve = NDSolve{D[y[x, t], x, x]-D[y[x, t], t,
> t]/(c[x]*c[x])-D[y[x,t],t]/R==0,
>     y[x, 0] == 0, Derivative[0,1][y][x, 0] == 0,
>        y[0, t] == Cos[t],
>        y[1, t]==Exp[-1]}, y, {x, 0, 1}, {t, 0, 2*Pi}]
> 
> I received the message: <Equations may not give solutions for all
> "solve" variables>
> After further "research" I have discovered none solution was given
> 
> Real "R" (instead of complex) do not change anything.
> 
> My question is:
> Is mathematica able to solve such simple equations? Any help?


First of all, the correct syntax for a second partial dervative is,

            D[D[y[x,t],x],x] 
and not
 
           D[y[y,t],x,x]

as you've written.

Secondly, you must change the "if" in your if[.. statement to "If" with
a capital "I". 

With these changes you should get a solution in the form

{{y -> InterpolatingFunction[{{0, 1.}, {0., 6.28319}},<>]}}

Hope this helps,
   Bill



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