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Derive a solution to the initial-boundary value problem: Ut +u – Uzz = Y(x, t), 0 0 u(0, t) = A(t), uz (1, t) = B(t), u(x,0) = 9(x), t>0 0 < x <1 Hint: Look for a function v(x, t) so that the function w(x, t) solves a problem of the form in question 2, where u(x, t) = v(x, t) + w(x, t). Then use the result from question 2.

Derive a solution to the initial-boundary value problem: Ut +u – Uzz = Y(x, t), 0 0 u(0, t) = A(t), uz (1, t) = B(t), u(x,0) = 9(x), t>0 0 < x <1 Hint: Look for a function v(x, t) so that the function w(x, t) solves a problem of the form in question 2, where u(x, t) = v(x, t) + w(x, t). Then use the result from question 2.

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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Derive a solution to the initial-boundary value problem: Ut +u – Uzz = r(x, t), 0< x < 1, t> 0 u(0, t) = A(t), uz (1, t) = B(t), t>0 u(x, 0) = g(x), 0 < x <1 Hint: Look for a function v(x, t) so that the function w(x, t) solves a problem of the form in question 2, where u(x, t) = v(x, t) + w(x, t). Then use the result from question 2.
Transcribed Image Text:Derive a solution to the initial-boundary value problem: Ut +u – Uzz = r(x, t), 0< x < 1, t> 0 u(0, t) = A(t), uz (1, t) = B(t), t>0 u(x, 0) = g(x), 0 < x <1 Hint: Look for a function v(x, t) so that the function w(x, t) solves a problem of the form in question 2, where u(x, t) = v(x, t) + w(x, t). Then use the result from question 2.
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