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Re: Partial Differential Equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg92872] Re: Partial Differential Equations
  • From: dh <dh at metrohm.ch>
  • Date: Thu, 16 Oct 2008 05:05:33 -0400 (EDT)
  • References: <gd4dm4$bh7$1@smc.vnet.net>


Hi Sergio,

you need enough boundary conditions to ensure that your problem has a 

unique answer. E.g. ypu may request that the string is fixed at bouth 

ends. Then you can set up the equations like:

eq={

D[u[x,t],{t,2}] == D[u[x,t],{x,2}] ,

u[x,0]== Sin[x],

Derivative[0,1][u][x,0]==0,

u[0,t]==0,

u[Pi,t]==0

};

sol=u/.NDSolve[eq,u,{x,0,Pi},{t,0,10}][[1]]

Plot3D[sol[x,t],{x,0,Pi},{t,0,10}]

hope this helps, Daniel



Sergio Miguel Terrazas Porras wrote:

> Hello Group:

> 

> 

> 

> Hill someone please post an example for solving with Mathematica v. 6 a

> partial differential equation with boundary conditions ?

> 

> 

> 

> Say, the one dimensional wave equation for a string with fixed ends and

> initial condition u(x,0) = f(x) and initial velocity u'(x,0) = 0.

> 

> 

> 

> The documentation exemplifies only the general solution. When I try to

> include the boundary and initial conditions it does not solve it.

> 

> 

> 

> Thanks in advance.

> 

> 

> 

> Dr. Sergio Terrazas

> 

> University of Juarez

> 

> Chihuahua, Mexico

> 

> 

> 





-- 



Daniel Huber

Metrohm Ltd.

Oberdorfstr. 68

CH-9100 Herisau

Tel. +41 71 353 8585, Fax +41 71 353 8907

E-Mail:<mailto:dh at metrohm.com>

Internet:<http://www.metrohm.com>




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