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Consider the wave equation Utt- c²Uxx = 0 ᏆᏆ the half-line x = [0, ∞) with boundary condition U (0, t) = 0 d initial conditions U(x,0) = f(x), Ut(x,0) = g(x). this problem we construct the solution to the above problem using even extensions. For s, let F(x) = { √(-²2) +²0 + f(x) x>0 1

Consider the wave equation Utt- c²Uxx = 0 ᏆᏆ the half-line x = [0, ∞) with boundary condition U (0, t) = 0 d initial conditions U(x,0) = f(x), Ut(x,0) = g(x). this problem we construct the solution to the above problem using even extensions. For s, let F(x) = { √(-²2) +²0 + f(x) x>0 1

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 wave equation Utt - c²Uxx 1 the half-line x = [0, ∞) with boundary condition Ux(0, t) = 0 nd initial conditions 0 U(x,0) = f(x), Ut(x,0) = g(x). this problem we construct the solution to the above problem using even extensions. For is, let F(x) = { {(2)) +²0 + f(x) x>0 f(-x) x<0' 1
Transcribed Image Text:Consider the wave equation Utt - c²Uxx 1 the half-line x = [0, ∞) with boundary condition Ux(0, t) = 0 nd initial conditions 0 U(x,0) = f(x), Ut(x,0) = g(x). this problem we construct the solution to the above problem using even extensions. For is, let F(x) = { {(2)) +²0 + f(x) x>0 f(-x) x<0' 1
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