P₁ For u(x,t) defined on the domain of 0 ≤x≤ 2023 and t≥ 0, solve the PDE, et Ju 2²u at · + π²u, əx² with the boundary conditions, (i) u (0, t) = 0, (ii) u(2023, t) = 0, (iii) u(x, 0) = sin(x) + sin(2x).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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P₁
For u(x,t) defined on the domain of 0≤x≤2023 and t≥ 0, solve the PDE,
ди
et.
at
=
²u
əx²
+π²u,
with the boundary conditions,
(i) u (0, t) = 0, (ii) u (2023, t) = 0, (iii) u(x, 0) = sin(x) + sin(2лx).
Transcribed Image Text:P₁ For u(x,t) defined on the domain of 0≤x≤2023 and t≥ 0, solve the PDE, ди et. at = ²u əx² +π²u, with the boundary conditions, (i) u (0, t) = 0, (ii) u (2023, t) = 0, (iii) u(x, 0) = sin(x) + sin(2лx).
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