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1. Consider the heat equation du = k for - T 0 | with the periodic boundary conditions и(-п,t) — и(п, t) and du (-п,t) - du (7T, t), for t > 0, -IT and the initial value condition u(x, 0) = f(x) for æ E [-7, 7]. Solve for the following initial value conditions: a) f(x) = So re (-7,0] x € x € (0, 7) b) f(x) =

1. Consider the heat equation du = k for - T 0 | with the periodic boundary conditions и(-п,t) — и(п, t) and du (-п,t) - du (7T, t), for t > 0, -IT and the initial value condition u(x, 0) = f(x) for æ E [-7, 7]. Solve for the following initial value conditions: a) f(x) = So re (-7,0] x € x € (0, 7) b) f(x) =

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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1. Consider the heat equation ди = k for - T<x < T, and t > 0 | with the periodic boundary conditions u(-7, t) = u(1, t) and du (-7,t) = du (7T, t), for t > 0, and the initial value condition u(x, 0) = f(x) for x E [-7, 7]. Solve for the following initial value conditions: a) f(x) = x So re (-7,0]| x € а€ (0, т) b) f(x) =
Transcribed Image Text:1. Consider the heat equation ди = k for - T<x < T, and t > 0 | with the periodic boundary conditions u(-7, t) = u(1, t) and du (-7,t) = du (7T, t), for t > 0, and the initial value condition u(x, 0) = f(x) for x E [-7, 7]. Solve for the following initial value conditions: a) f(x) = x So re (-7,0]| x € а€ (0, т) b) f(x) =
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