Comments on: Separation of variables, or how I’m learning to ignore the math, and just take the Fourier expansion http://www.tangentspace.net/cz/archives/2007/04/if-we-ignore-the-math-it-all-makes-sense/ somewhere near the beginning. Mon, 01 Dec 2008 21:09:40 +0000 http://wordpress.org/?v=2.5 By: Alex http://www.tangentspace.net/cz/archives/2007/04/if-we-ignore-the-math-it-all-makes-sense/#comment-125135 Alex Thu, 19 Apr 2007 14:29:52 +0000 http://www.tangentspace.net/cz/archives/2007/04/if-we-ignore-the-math-it-all-makes-sense#comment-125135 I used Fourier basis functions: a change of variables to get the pde in terms of a function with homogeneous BCs, assumed the solution was a fourier series with time varying coefficients, and used the initial conditions and the source terms determine them. I don't know anything much about green's functions-- I think we'll cover those soon. But I remember Kevorkian's analytic solutions book talking about the relationship b/w green's functions and separation of variables-- there might have been something on green's functions for inhomogeneous BCs. I used Fourier basis functions: a change of variables to get the pde in terms of a function with homogeneous BCs, assumed the solution was a fourier series with time varying coefficients, and used the initial conditions and the source terms determine them. I don’t know anything much about green’s functions– I think we’ll cover those soon. But I remember Kevorkian’s analytic solutions book talking about the relationship b/w green’s functions and separation of variables– there might have been something on green’s functions for inhomogeneous BCs.

]]> By: ObsessiveMathsFreak http://www.tangentspace.net/cz/archives/2007/04/if-we-ignore-the-math-it-all-makes-sense/#comment-125060 ObsessiveMathsFreak Thu, 19 Apr 2007 11:55:10 +0000 http://www.tangentspace.net/cz/archives/2007/04/if-we-ignore-the-math-it-all-makes-sense#comment-125060 So what did you use? Green's functions? Fourier basis functions? Are you supposed to assume that Q(x,t) is separable as well? Not sure how you go about getting a green's function for inhomogeneous boundary conditions. The only ones I use are green's function that simply must tend to zero as x goes to infinity. So what did you use? Green’s functions? Fourier basis functions? Are you supposed to assume that Q(x,t) is separable as well?

Not sure how you go about getting a green’s function for inhomogeneous boundary conditions. The only ones I use are green’s function that simply must tend to zero as x goes to infinity.

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