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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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