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- 1. u(x, 0) - 50, 0

- 1. u(x, 0) - 50, 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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Consider the conduction of heat in a rod 60 cm in length whose ends are maintained at 0°C for all t> 0. Find an expression for the temperature u(x, t) if the initial temperature distribution in the rod is the given function. Suppose that a - 1. u(x, 0) - 50, 0<x < 60 For t = 5 and x = 30 determine how many non-zero terms are needed to find the solution correct to three decimal places. A reasonable way to do this is to find n so that including one more term does not change the first three decimal places of u(30, 5). (A computer algebra system n = recommended.) Repeat for t- 30. n = Repeat for t- 120. n = Form a conclusion about the speed of convergence of the series for u(x, t). o The series solution converges faster as t increases. The series solution converges slower as t increases. The series solution converges at the same speed for all t. Additional Materials
Transcribed Image Text:Consider the conduction of heat in a rod 60 cm in length whose ends are maintained at 0°C for all t> 0. Find an expression for the temperature u(x, t) if the initial temperature distribution in the rod is the given function. Suppose that a - 1. u(x, 0) - 50, 0<x < 60 For t = 5 and x = 30 determine how many non-zero terms are needed to find the solution correct to three decimal places. A reasonable way to do this is to find n so that including one more term does not change the first three decimal places of u(30, 5). (A computer algebra system n = recommended.) Repeat for t- 30. n = Repeat for t- 120. n = Form a conclusion about the speed of convergence of the series for u(x, t). o The series solution converges faster as t increases. The series solution converges slower as t increases. The series solution converges at the same speed for all t. Additional Materials
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