My Math Forum analytical solution to BVP with fu'n and 2nd dr'tve of fu'n

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 June 13th, 2012, 10:19 AM #1 Newbie   Joined: May 2012 Posts: 3 Thanks: 0 analytical solution to BVP with fu'n and 2nd dr'tve of fu'n I have the following (fairly simple) boundary value problem and I am trying to find an analytical solution to it, but for the life of me it's not working out. This is part of a larger thing where I'm trying to understand FEM and BVPs. Essentially this is a diffusion reaction problem. My problem is I have the following (?=pi) v-kv''=f(x)=sin(?x), x is between 1 and 2 v@x=0 = 0 and v@x=1 = 0 I have some plots but they are not matching my analytical solution (I think my brain has just broken tonight), but if anyone can steer me right I'd be grateful.
 June 13th, 2012, 10:21 AM #2 Newbie   Joined: May 2012 Posts: 3 Thanks: 0 Re: analytical solution to BVP with fu'n and 2nd dr'tve of f I should also have mentioned k is a constant
 June 13th, 2012, 12:02 PM #3 Global Moderator   Joined: Dec 2006 Posts: 20,635 Thanks: 2080 I assume k is positive. WA gives v = Ae^(x/?k) + Be^(-x/?k) + sin(?x)/(?²k + 1), where A and B are constants chosen so that the boundary conditions are satisfied.

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