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Separating functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128456] Separating functions
  • From: carlos at colorado.edu
  • Date: Sun, 21 Oct 2012 02:10:36 -0400 (EDT)
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Hi,

I have a problem in identification.  In the middle of the solution of a wave propagation problem on a regular lattice using a separation-of-variables method, I get a function of the form

               F(x,y,t)= f(x,y) g(t)

in which x,y are space coordinates and t is time. Both can be very complicated and vary from problem to problem, but Mathematica' Simplify is able to factor them. Here is a fairly trivial 1D example with an F output by //InputForm:


      Bx*(-5*Em - 3*Em*=CE=BD + 2*a^2*=CF=81*=CF=89^2 - 2*a^2*=CE=BD^2*=CF=81*=CF=89^2 + 4*Em*(1 + =CE=BD)*Cos[(a*kx)/
          Sqrt[2]] - Em*(-1 + =CE=BD)*Cos[Sqrt[2]*a*kx])*(Cos[t*=CF=89] - I*Sin[t*=CF=89]))/(2*c0^2*(-1 + =CE=BD^2)*=CF=81)

Here g(t)=(Cos[t*=CF=89] - I*Sin[t*=CF=89])). For more complicated 2D cases, F(x,y,t) becomes a array of product functions, each taking 20-30 lines.

Question: is there a way to separate  f(x,y) and g(t) that does not require external intervention?

Thanks.



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