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Ex. 4. Find a solution of Laplace's equation, u̟ +u„=0, inside the rectangle 0

Ex. 4. Find a solution of Laplace's equation, u̟ +u„=0, inside the rectangle 0

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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Ex. 4. Find a solution of Laplace's equation, u„ +u„=0, inside the rectangle 0<x<a, 0<y<b, subject to the following boundary conditions: и(0, у) %3 0, и(а, у) - 0, 0<у<b а. и(х,0) — Һ(х), и(х,b) - 0, 0sxsa' и(0, у) %3 0, и(а, у) - S0), 0<y<b b. и(х,0) %3D h(х), и(х,b) - 0, 0sxsa'" и(0), у) — Ф(у), и(а, у) — /(), 0<у<b и(х,0) %3D h(x), и(х,b) %—D g(x), 0sxsa" с.
Transcribed Image Text:Ex. 4. Find a solution of Laplace's equation, u„ +u„=0, inside the rectangle 0<x<a, 0<y<b, subject to the following boundary conditions: и(0, у) %3 0, и(а, у) - 0, 0<у<b а. и(х,0) — Һ(х), и(х,b) - 0, 0sxsa' и(0, у) %3 0, и(а, у) - S0), 0<y<b b. и(х,0) %3D h(х), и(х,b) - 0, 0sxsa'" и(0), у) — Ф(у), и(а, у) — /(), 0<у<b и(х,0) %3D h(x), и(х,b) %—D g(x), 0sxsa" с.
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