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4.2 Find the solution subject to the following boundary and initial conditions of the heat equation, u = a²uxx- (a) u(0, t) = u(1,t) = 0, u(x,0)=z,0

4.2 Find the solution subject to the following boundary and initial conditions of the heat equation, u = a²uxx- (a) u(0, t) = u(1,t) = 0, u(x,0)=z,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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4.2 Find the solution subject to the following boundary and initial conditions of the heat equation, u = a²uxx- (a) u(0, t) = u(1,t) = 0, u(x,0) = x, 0<x< 1 [1 if 0<x< 1 (b) u(0, t) = u(2, t) = 0, u(x,0) = 0 if 1 < x < 2 (uz (0, t)= (10e-0.1t) if t≥ 0 (c) u (1,t) = 0 if t ≥ 0 u(x,0) = 0 if 0 ≤ x ≤ 1 (u₂(0, t) = -1 ift 20 (d)u(1,t) + uz (1,t) = 0 ift> 0 u(x,0) = 0 if 0 ≤ x ≤1
Transcribed Image Text:4.2 Find the solution subject to the following boundary and initial conditions of the heat equation, u = a²uxx- (a) u(0, t) = u(1,t) = 0, u(x,0) = x, 0<x< 1 [1 if 0<x< 1 (b) u(0, t) = u(2, t) = 0, u(x,0) = 0 if 1 < x < 2 (uz (0, t)= (10e-0.1t) if t≥ 0 (c) u (1,t) = 0 if t ≥ 0 u(x,0) = 0 if 0 ≤ x ≤ 1 (u₂(0, t) = -1 ift 20 (d)u(1,t) + uz (1,t) = 0 ift> 0 u(x,0) = 0 if 0 ≤ x ≤1
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