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KERCISE 4. Solve the following PDE: Urr + Uyy = 0, u(x,0) = 0, u(0, y) = 0, 0

KERCISE 4. Solve the following PDE: Urr + Uyy = 0, u(x,0) = 0, u(0, y) = 0, 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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EXERCISE 4. Solve the following PDE: 0 < x, y < 1, 0 < x < 1, Uxx + Uyy = 0, u(x, 0) = 0, u(0, y) = 0, 0 < y < 1, u(x, 1) = f(x), 0 < x < 1, u(1, y) = g(y), 0 < y < 1. Find the solution when f(x) = sin(x) and g(y) = sin(Ty) cos(Ty). Hint: Show first that you can write u(x, y) = v(x, y) + w(x, y), where v(x, y) and w(x, y) solve the same PDE but with only one non-zero boundary term.
Transcribed Image Text:EXERCISE 4. Solve the following PDE: 0 < x, y < 1, 0 < x < 1, Uxx + Uyy = 0, u(x, 0) = 0, u(0, y) = 0, 0 < y < 1, u(x, 1) = f(x), 0 < x < 1, u(1, y) = g(y), 0 < y < 1. Find the solution when f(x) = sin(x) and g(y) = sin(Ty) cos(Ty). Hint: Show first that you can write u(x, y) = v(x, y) + w(x, y), where v(x, y) and w(x, y) solve the same PDE but with only one non-zero boundary term.
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