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MathGroup Archive 2000

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Re: Solve[wave equation,bound.cond.]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg21545] Re: Solve[wave equation,bound.cond.]
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Fri, 14 Jan 2000 02:44:05 -0500 (EST)
  • Organization: University of Western Australia
  • References: <85i0ed$1od@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Karkaletsis Angelos wrote:

> I am trying to get the analytical solution of
> du/dt+c*du/dx=0,u[0,t]=a,u[x,0]=b, a,b real, but i can't.Does anybody
> know?

Dropping the boundary conditions, you can determine the general
solution:

  In[1]:= u[x_, t_] = u[x, t] /.
   First[DSolve[D[u[x, t], x] + c*D[u[x, t], t] == 0, u[x, t], {x, t}]]

  Out[1]= C[1][t - c*x]

C[1] is an arbitrary function. Supplying the boundary conditions you
should be able to
work out what is going on:

  In[2]:= {u[0, t] == a, u[x, 0] == b}
  Out[2]= {C[1][t] == a, C[1][-c*x] == b}

Cheers,
    Paul




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