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Consider the following heat equation problem ди 1 + 5 (Əx? -T < x < T, 0< y< 1, t> 0, u(-n, y, t) = u(T , Y, t), -т, у, t) - du (1, y, t), du (x, 0, t) = u(x, 1, t) = 0, u(x, y,0) = f(x, y). a) Interpret the physical boundary value problem. b) Solve the problem using separation of variables. For full marks you are required to show the steps leading to the space and temporal sub-problems. You may use the formula solution for the corresponding Sturm-Liouville problems.

Consider the following heat equation problem ди 1 + 5 (Əx? -T < x < T, 0< y< 1, t> 0, u(-n, y, t) = u(T , Y, t), -т, у, t) - du (1, y, t), du (x, 0, t) = u(x, 1, t) = 0, u(x, y,0) = f(x, y). a) Interpret the physical boundary value problem. b) Solve the problem using separation of variables. For full marks you are required to show the steps leading to the space and temporal sub-problems. You may use the formula solution for the corresponding Sturm-Liouville problems.

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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Consider the following heat equation problem ²u + ди 1 -T < x < T, 0<y<1, t> 0, 5 ( Əx2 dy? u(-п, у, t) — и(т, у, t), ди (-п,у, t) - ди (T, Y, t), ди (x,0, t) = u(x, 1, t) = 0, dy u(x, y,0) = f(x, y). a) Interpret the physical boundary value problem. b) Solve the problem using separation of variables. For full marks you are required to show the steps leading to the space and temporal sub-problems. You may use the formula solution for the corresponding Sturm-Liouville problems.
Transcribed Image Text:Consider the following heat equation problem ²u + ди 1 -T < x < T, 0<y<1, t> 0, 5 ( Əx2 dy? u(-п, у, t) — и(т, у, t), ди (-п,у, t) - ди (T, Y, t), ди (x,0, t) = u(x, 1, t) = 0, dy u(x, y,0) = f(x, y). a) Interpret the physical boundary value problem. b) Solve the problem using separation of variables. For full marks you are required to show the steps leading to the space and temporal sub-problems. You may use the formula solution for the corresponding Sturm-Liouville problems.
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