22. Solve the following Dirichlet problems: (a) V²u = 0, u (x,0) = x (x - 1), u (0, y) = 0, 0 < x < 1, u (x, 1) = 0, u (1, y) = 0, 0 < y < 1, 0≤x≤ 1, 0 ≤ y ≤ 1.
22. Solve the following Dirichlet problems: (a) V²u = 0, u (x,0) = x (x - 1), u (0, y) = 0, 0 < x < 1, u (x, 1) = 0, u (1, y) = 0, 0 < y < 1, 0≤x≤ 1, 0 ≤ y ≤ 1.
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:22. Solve the following Dirichlet problems:
V²u = 0,
(a)
0 < x < 1,
0 < y < 1,
u (x, 0) = x (x – 1) ,
u (x, 1) = 0,
0 < x< 1,
u (0, y) = 0,
и (1, у) — 0,
0 < y< 1.
(d)
V²u = 0,
0 < x < 1,
0 < y < 1,
и (х, 0) %3D 0,
u (x, 1) = 0,
0 < x < 1,
u (0, y) = 0,
u (1, y) = sin TY COS TY,
0 <y < 1.
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