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# Class Note for ECE 449 at UA

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COURSE
PROF.
No professor available
TYPE
Class Notes
PAGES
2
WORDS
KARMA
25 ?

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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 15 views.

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Date Created: 02/06/15
Method of Separation of Variables Application to Diffusion Equa on Rajanikanth Jammalamadaka November 77 2005 1 Method of separation of variables The diffusion equation is given by at c um with boundary conditions u 0 t 0 7 u L7 t 0 and initial condition M In the method of separation of variables7 we assume that Mm t Mm Ct gtmmm wa yow WW GW 7A 0 an new gt Now7 we have two equations G t 7A c Ct whose solution is given by owikm n and whose solution is given by Mm clcos x 628inX Since the boundary conditions are purely dependent upon x7 they can be re written as ltIgt 0 0 and lt1gt L 0 Applying this to equation 27 we get Mm clcos Combining 1 and 37 we have the solution for the diffusion equation as 00 7747f Mm t 2Ancosfm e quot39c39t n In order to nd the coefficients An7 we will make use of the orthogonality relation L mm 7mm 3087608 dm 0 L ny m nm 0 nm0 brain 0 Using this relation7 we get Am fOL 7710 fOL fmcosm mdm m 21

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