Solve the wave equation on the half line with the Utt – cʻuxx = 0, x> 0, t > 0 и, (0, 1) %3D h(), 1>0 и(х,0) %3D и,(х,0) %3D 0, х>0. х> 0, 1> 0 .

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Question 7
Solve the wave equation on the half line with the Neumann boundary
condition
Utt – c²uxx = 0, x > 0, t > 0
и, (0, г) %3D h(t), 1>0
и(х,0) %3 и, (х,0) %3 0, х> 0.
(Hint: Use the general formula u(x, t) = f(x+ct)+g(x – ct). You only need to solve for formulas
for f and g in terms of the function h, i.e. you don't need to discuss the different cases of the
piecewise defined function.)
Transcribed Image Text:Question 7 Solve the wave equation on the half line with the Neumann boundary condition Utt – c²uxx = 0, x > 0, t > 0 и, (0, г) %3D h(t), 1>0 и(х,0) %3 и, (х,0) %3 0, х> 0. (Hint: Use the general formula u(x, t) = f(x+ct)+g(x – ct). You only need to solve for formulas for f and g in terms of the function h, i.e. you don't need to discuss the different cases of the piecewise defined function.)
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