Exercise 4: Solve the heat equation on the square [0, 7] × [0, T] subject to the following bound-ary/initial conditions:U-(0, y, t) = u=(T, Y, t) = 0,U,(x, 0, t) = u,(x, T, t) = 0,u(r, y,0) = ry(1 – x)(1 – y).

We have to solve the heat equation ∂u∂t=∂2u∂x2+∂2u∂y2 -------…

Answered: Exercise 4: Solve the heat equation on…

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 heat equation on the square [0, 7] × [0, 7] subject to the following bound- ary/initial conditions: (u (0, y, t) = u,(7 , Y, t) = 0, и, (г, 0, 1) %3D и, (т, п, [) — 0, u(х, у, 0) — ту(1 — г)(1 — у). -