Galerkin Method for ODEs

[flipdeadshot22]

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Anyone familiar with this? My book isn't very clear, and my wonderful professor basically puts the book on a Powerpoint and uses that for his lectures.

[tangent] Why the hell do professors do that? We already have the damn book...this is no help to us, and Powerpoint lectures just make everyone fall asleep![/tangent]

Anyway here's the problem I have to solve using the weak form, and a linear polynomial ( u(x)=a1x+a0 ):

u''+xu'=2u-1

0<x<1

u(0)=2
u(1)=u'(1)


Any strong hints to point me in the right direction would be greatly appreciated. Thank you.

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Well I never really got around to taking any formal classes on DE's (Physics is pretty much all linear PDEs so that's my expertise) but from the tidbits i've picked up in solving related problems, i'd solve the homogenous part of the equation using a power series solution and generate a recursive relation for the coefficients; but from the looks of it your teacher wants you to use Galerikins methods. I'll take a look at an old undergrad DE book, they have a pretty good section on this technique i believe. This looks like a pretty useful method in computational problems from what I was able to glean from wiki.