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MathGroup Archive 1999

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Re: How can I do this?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19155] Re: How can I do this?
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 5 Aug 1999 23:58:58 -0400
  • Organization: Universitaet Leipzig
  • References: <7obbiv$3rm@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Bill, 

it depend on the problem. Ifthe 2d problem can be transformed to a
rectangular domain 

f[t,x]=Sum[ c[i,j] p[j,t] g[j,x], {i,0,n1},{j,0,n2}]

(notice the product form of the basis function) thats the
way how partial differential equations solved by Fourier expansion.

If you can't get a rectangular domain

f[t,x]=Sum[c[i,j] b[i,j,t,x],{i,0,n1},{j,0,n2}]

will be more general. How ever you will have problems to
find an orthogonal basis b[i,j,t,x].

Hope that helps
  Jens

> My question is, How do I go about constructing a function similar to the one
> above but now of two variables so that in the expansion
> 
>                                f[t,  x] = c[1] p[1, x]+c[2]p[2, x] + ...
> 
> the c's are functions of t  so that formal differentiations and integrations
> with respect to t can be carried out on it.
> 
> Thanks,
> 
>    Bill Bertram


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