Find the solution for the following one-dimensional heat equation: U = ku 0 0, %3D
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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Question
Transcribed Image Text:(1) Find the solution for the following one-dimensional heat equation:
0 <x < L,t > 0,
u(0, t) = 0,
t> 0,
u,(L, t) = 0,
t> 0,
u(x,0) = f(x),
0 <r < L.
Expert Solution
Step 1
In this question, we solve the 1-D heat equation
here we use the method of separation of the variable
u(x,t)=X(x).T(t)
Step by step
Solved in 2 steps with 1 images
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