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1. Find the heat kernel for the half-line, x ≥ 0, and use it to solve the IVP, 1 IC BC Ut = u(x,0) = = -Uxx9 f(x), 0₁ XER+, tER+ ux(0,t) teR+ This is an example of Kelvin's method of images. XER+

1. Find the heat kernel for the half-line, x ≥ 0, and use it to solve the IVP, 1 IC BC Ut = u(x,0) = = -Uxx9 f(x), 0₁ XER+, tER+ ux(0,t) teR+ This is an example of Kelvin's method of images. XER+

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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1. Find the heat kernel for the half-line, x ≥ 0, and use it to solve the IVP, 1 IC BC Ut u(x, 0) = = -Uxx = 2 f(x), XER+, tER+ XER+ ux(0,t) 0, teR+ This is an example of Kelvin's method of images.
Transcribed Image Text:1. Find the heat kernel for the half-line, x ≥ 0, and use it to solve the IVP, 1 IC BC Ut u(x, 0) = = -Uxx = 2 f(x), XER+, tER+ XER+ ux(0,t) 0, teR+ This is an example of Kelvin's method of images.
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