Use the superposition principle to solve Laplace's equation (1) in Section 12.5 a²u a²u + -0, 0
Use the superposition principle to solve Laplace's equation (1) in Section 12.5 a²u a²u + -0, 0
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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Transcribed Image Text:Use the superposition principle to solve Laplace's equation (1) in Section 12.5
a²u a2u
+ -0, 0<x<a, 0 <y<b (1)
ax² dy²
for a square plate subject to the given boundary conditions.
u(0, y) = 0,
u(2, y) = y(2-y)
{x,
0 < x < 1
u(x, 2)
(2-x, 1<x<2
· Σ(Γ
u(x, 0) 0,
-
u(x, y) = 0
4
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