Solve Laplace's equation, u(0, y) = 0, u(x, 0) = f(x), u(x, y) = 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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Nn.106.
Subject :- Advance Mathematic
![Solve Laplace's equation,
u(0, y) = 0,
u(x, 0) = f(x),
u(x, y) =
a²u a²u
əx² Əy²
u(a, y) = 0
u(x, b) = 0
= 0, 0<x<a, 0 <y<b, (see (1) in Section 12.5) for a rectangular plate subject to the given boundary conditions.
+ Ž[A₂ ([
n = 1
)]
- ²-² f(x) sin(x) dx
where An =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a79f5fd-2bdd-484b-9c0d-a83d48b55247%2Ff5aeb20d-f06e-40f9-b56c-2d31217da592%2Fs3o4gwd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Solve Laplace's equation,
u(0, y) = 0,
u(x, 0) = f(x),
u(x, y) =
a²u a²u
əx² Əy²
u(a, y) = 0
u(x, b) = 0
= 0, 0<x<a, 0 <y<b, (see (1) in Section 12.5) for a rectangular plate subject to the given boundary conditions.
+ Ž[A₂ ([
n = 1
)]
- ²-² f(x) sin(x) dx
where An =
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