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We are given the following heat equation on a 1-dimensional ring. D It has periodic boundary conditions u(−1,t) = u(1,t), ur (−1,t) — uz (1,t) with initial condition u(x, 0) = x² (1) Express the solution as a series form. (2) Determine the coefficients of the series. (3) Plot the solution using a sufficient number of terms from the series.

We are given the following heat equation on a 1-dimensional ring. D It has periodic boundary conditions u(−1,t) = u(1,t), ur (−1,t) — uz (1,t) with initial condition u(x, 0) = x² (1) Express the solution as a series form. (2) Determine the coefficients of the series. (3) Plot the solution using a sufficient number of terms from the series.

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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We are given the following heat equation on a 1-dimensional ring. du DO Ət It has periodic boundary conditions - u(−1,t) = u(1,t), u (−1,t) – ủ (1,t) with initial condition u(x,0) = x² (1) Express the solution as a series form. (2) Determine the coefficients of the series. (3) Plot the solution using a sufficient number of terms from the series.
Transcribed Image Text:We are given the following heat equation on a 1-dimensional ring. du DO Ət It has periodic boundary conditions - u(−1,t) = u(1,t), u (−1,t) – ủ (1,t) with initial condition u(x,0) = x² (1) Express the solution as a series form. (2) Determine the coefficients of the series. (3) Plot the solution using a sufficient number of terms from the series.
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