My Math Forum Solving for PDE Eigenvalues

 Differential Equations Ordinary and Partial Differential Equations Math Forum

February 23rd, 2017, 02:13 PM   #1
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Solving for PDE Eigenvalues

Eigenvalue PDE? How can I solve for lambda of the new problem exactly how the old problem was solved. Both problems are included in the attached picture. Please show steps
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 February 23rd, 2017, 06:11 PM #2 Senior Member     Joined: Sep 2015 From: CA Posts: 914 Thanks: 494 any chance you could upload a version of that image that doesn't require a microscope to see? Thanks from Joppy
February 23rd, 2017, 08:47 PM   #3
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From: College Station

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Picture is in Zipfile

Don't know how to upload image any larger. Site has a limit. I placed it in the zipfile attached.
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 mymathforum.zip (29.9 KB, 1 views)

 February 25th, 2017, 04:45 AM #4 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,279 Thanks: 570 And opening THAT requires one to have Microsoft Office on your computer! Using a magnifying glass to read the first post, the first problem given is the boundary value problem $\frac{\partial^2 u}{\partial x^2}+ \frac{\partial^2 u}{\partial u^2}= f(x, y)= -x$ with boundary conditions u(x, 0)= u(x, W)= 0, u(0, y)= u(L, y)= 0. The "suggest" first solving the eigenvalue problem $\frac{\partial^2 u}{\partial x^2}+ \frac{\partial^2 u}{\partial u^2}= -\lambda u$. The question, then, is "why doesn't that same eigenvalue strategy work if the boundary value problem is $\frac{\partial^2 u}{\partial x^2}+ \frac{\partial^2 u}{\partial u^2}+ k^2u= f(x, y)= -x$ with boundary conditions u(x, 0)= u(x, W)= 0, u(0, y)= u(L, y)= 0."

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