Class Note for ECE 449 at UA
Popular in Course
Popular in Department
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.
Reviews for Class Note for ECE 449 at UA
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
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
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'