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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- Delivered-to: l-mathgroup@wolfram.com
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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.