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Solve the Neumann problem for the wave equation on the half line 0<x<infinity.

Here is what I have

[tex]U_{tt}=c^{2}U_{xx}[/tex]

Initial conditions

[tex]U(x,0)=\phi(x)[/tex]

[tex]U_{t}(x,0)=\psi(x)[/tex]

Neumann BC

[tex]U_{x}(0,t)=0[/tex]

So I extend [tex]\phi(x)[/tex] and [tex]\psi(x)[/tex] evenly and get:

[tex]\phi_{even}(x)={^{\phi(x) for x\geq 0}_{\phi(-x) for x\leq 0}[/tex]

[tex]\psi_{even}(x)={^{\psi(x) for x\geq 0}_{\psi(-x) for x\leq 0}[/tex]

I'm not sure what to do from here. I know the d'Alembert equation, but just plugging in phi even and psi even doesn't make much sense to me as the solution seems too general.

I'm also not too comfortable with the meaning behind the boundary conditions, so if you can dumb down your answers, I'd be appreciative.

Thanks!

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# Homework Help: Wave equation with Neumann BDC

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