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June 13th, 2012, 11:19 AM   #1
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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.
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June 13th, 2012, 11:21 AM   #2
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Re: analytical solution to BVP with fu'n and 2nd dr'tve of f

I should also have mentioned k is a constant
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June 13th, 2012, 01:02 PM   #3
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I assume k is positive. WA gives v = Ae^(x/?k) + Be^(-x/?k) + sin(?x)/(?k + 1), where A and B are constants chosen so that the boundary conditions are satisfied.
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