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Question 4. Consider the equation и, — ихх — их 3D 0, 0<х<1,t> 0 u(0, 1) %3D 0, и(1,1) %3D 1, 1> 0, и(х,0) — 0, 0

Question 4. Consider the equation и, — ихх — их 3D 0, 0<х<1,t> 0 u(0, 1) %3D 0, и(1,1) %3D 1, 1> 0, и(х,0) — 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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Question 4. Consider the equation Ит — ихх — их —D 0, 0 < x < 1, t > 0 и(0, 1) %3 0, и(1,г) — 1, г> 0, и(х,0) — 0, 0 <x<л. (a) Consider the change of coordinates u(x,t) = v(x,t)eax+br, and choose a, b to reduce the equation to a standard heat equation. (b) Solve the corresponding equation for v(x,t) using the Fourier series.
Transcribed Image Text:Question 4. Consider the equation Ит — ихх — их —D 0, 0 < x < 1, t > 0 и(0, 1) %3 0, и(1,г) — 1, г> 0, и(х,0) — 0, 0 <x<л. (a) Consider the change of coordinates u(x,t) = v(x,t)eax+br, and choose a, b to reduce the equation to a standard heat equation. (b) Solve the corresponding equation for v(x,t) using the Fourier series.
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