= 0,0 < x < a,0 < y < b dy dx² и(0, у) 3D 0, и(а, у) 3D 0,0 <у

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section: Chapter Questions
Problem 7CLR
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Question

Solve Laplace's equation with homogeneous vertical boundary conditions:

3 0,0 <x<а,0 <у<Ь
ду?
dx?
и(0, у) %3 0, и(а, у) %3D 0,0 <у<b
и(х, 0) %3D 1, и(х, b) — х,0 <х <а
From the previous problem we know that the PDE has the solution
2 (A, cosh() + B, sinh()) sin(*)-
пл
пл
n=1
with
a
2
An
sin(hpix)/a
dx %3D (2/(пр)(1-(-1)^n)
a
1
B, =
dx-
sin
%3D
Transcribed Image Text:3 0,0 <x<а,0 <у<Ь ду? dx? и(0, у) %3 0, и(а, у) %3D 0,0 <у<b и(х, 0) %3D 1, и(х, b) — х,0 <х <а From the previous problem we know that the PDE has the solution 2 (A, cosh() + B, sinh()) sin(*)- пл пл n=1 with a 2 An sin(hpix)/a dx %3D (2/(пр)(1-(-1)^n) a 1 B, = dx- sin %3D
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