2. Find a formal solution to the given initial-boundary value heat problem. Select two of the subprob- lems to complete. (a) homogeneous Dirichlet boundary heat problem u = 5u. 0 0, u(t,0) = u(1, 1) = 0, t>0, u(0, x) = (1 – x)x, 00 utt,0) = u(1,7) = 0, 1>0 u(0, x) = sin x, 00 u(1,0) = 5, u(1, 7) = 10, 1>0 u(0, x) = sin(3x) – sin(5x), 0

2. Find a formal solution to the given initial-boundary value heat problem. Select two of the subprob- lems to complete. (a) homogeneous Dirichlet boundary heat problem u = 5u. 0 0, u(t,0) = u(1, 1) = 0, t>0, u(0, x) = (1 – x)x, 00 utt,0) = u(1,7) = 0, 1>0 u(0, x) = sin x, 00 u(1,0) = 5, u(1, 7) = 10, 1>0 u(0, x) = sin(3x) – sin(5x), 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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Question

2. Find a formal solution to the given initial-boundary value heat problem. Select two of the subprob-
lems to complete.
(a) homogeneous Dirichlet boundary heat problem
U; = 5uxx, 0<x<1,t > 0,
u(t,0) = u(t, 1) = 0, t>0,
u(0, x) = (1 – x)x, 0<x<1.
(b) homogeneous Dirichlet boundary heat problem with source
U = 3uxx + x, 0<x<7, t >0
u(t,0) = u(1,7) =0, 1>0
u(0, x) = sin x, 0<x<A.
(c) non-homogeneous Dirichlet boundary heat problem
u = 2uxx 0<x<I,1>0
u(1,0) = 5, u(1, 71) = 10, t>0
u(0, x) = sin(3x) – sin(5.x), 0<x<
(d) homogeneous Neumann boundary heat problem
U = xx 0<x<A,1>0
u:(1,0) = u:(1, x) = 0, t>0
u(0, x) = e", 0<x<x.

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ISBN:

9780470458365

Author:

Erwin Kreyszig

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