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Solve the two-dimensional Laplace's equation J²u²u + dx² dy² 0 ≤ y ≤H, = cos I, subject to the boundary conditions (with respect to x) u(x,0) u(x, H) = 0 and the zero Dirichlet boundary conditions (with respect to y) u(0, y) = u(L, y) = 0, = 0, 0≤x≤L, a. by the method of separation of variables. b. by assuming that the solution u(x, y) has a Fourier sine series, that is, u(x, y) =B₁(y) sin(). n=1

Solve the two-dimensional Laplace's equation J²u²u + dx² dy² 0 ≤ y ≤H, = cos I, subject to the boundary conditions (with respect to x) u(x,0) u(x, H) = 0 and the zero Dirichlet boundary conditions (with respect to y) u(0, y) = u(L, y) = 0, = 0, 0≤x≤L, a. by the method of separation of variables. b. by assuming that the solution u(x, y) has a Fourier sine series, that is, u(x, y) =B₁(y) sin(). n=1

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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pls do a) and b)

Solve the two-dimensional Laplace's equation J² J²u + dx² dy² 0 ≤ y ≤H, = cos , subject to the boundary conditions (with respect to x) u(x,0) u(x, H) = 0 and the zero Dirichlet boundary conditions (with respect to y) u(0, y) = u(L, y) = 0, = 0, 0≤x≤L, a. by the method of separation of variables. b. by assuming that the solution u(x, y) has a Fourier sine series, that is, u(x, y) = [B₁(y) sin(72). n=1
Transcribed Image Text:Solve the two-dimensional Laplace's equation J² J²u + dx² dy² 0 ≤ y ≤H, = cos , subject to the boundary conditions (with respect to x) u(x,0) u(x, H) = 0 and the zero Dirichlet boundary conditions (with respect to y) u(0, y) = u(L, y) = 0, = 0, 0≤x≤L, a. by the method of separation of variables. b. by assuming that the solution u(x, y) has a Fourier sine series, that is, u(x, y) = [B₁(y) sin(72). n=1
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