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4. u(0, 1) = 0, u(π, t) = 0, t>0 0

4. u(0, 1) = 0, u(π, t) = 0, t>0 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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Answer question 4

In Problems 1-6, solve the heat equation (1) subject to the given conditions. 1. u(0, t) = 0, u(L, t) = 0, t> 0 u(x,0)= 100, 0<x<L 2 u(0, 1) = 0, u(L, t) = 0, t> 0 u(x,0) = x(L-x), 0<x<L 5. 6. au axx-o ax=L u(x, 0) = f(x), 0 < x < L dul ди x=0 = 0, = 0, u(x, 0) = axx-2 = 0, 1>0 = 0, 1>0 [x, 0<x<1 (0, 1<x<2 3. u(0, t) = 0, u(L, 1) = 0, t> 0 0<x<L/2 L/2<x<L u(π, t) = 0, t> 0 u(x, 0) = 4. u(0, 1) = 0, u(x, 0) (1, 10, = (T-X, -x, 0<x< π/2 π/2<x< T 13.3 Heat Equation 727 a²u ди ax² at u(-L, t) = u(L, 1), 1>0 ди -L<x<L, 1>0, ди ax |x=-L u(x, t) = f(x), -L<x<L. = , 1>0 axx=L See (15) in Section 12.5. Find the temperature u(x, Think full Fourier series 1
Transcribed Image Text:In Problems 1-6, solve the heat equation (1) subject to the given conditions. 1. u(0, t) = 0, u(L, t) = 0, t> 0 u(x,0)= 100, 0<x<L 2 u(0, 1) = 0, u(L, t) = 0, t> 0 u(x,0) = x(L-x), 0<x<L 5. 6. au axx-o ax=L u(x, 0) = f(x), 0 < x < L dul ди x=0 = 0, = 0, u(x, 0) = axx-2 = 0, 1>0 = 0, 1>0 [x, 0<x<1 (0, 1<x<2 3. u(0, t) = 0, u(L, 1) = 0, t> 0 0<x<L/2 L/2<x<L u(π, t) = 0, t> 0 u(x, 0) = 4. u(0, 1) = 0, u(x, 0) (1, 10, = (T-X, -x, 0<x< π/2 π/2<x< T 13.3 Heat Equation 727 a²u ди ax² at u(-L, t) = u(L, 1), 1>0 ди -L<x<L, 1>0, ди ax |x=-L u(x, t) = f(x), -L<x<L. = , 1>0 axx=L See (15) in Section 12.5. Find the temperature u(x, Think full Fourier series 1
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