Lecture Notes 7 -- Ex 3-4

[Shu Wang]

sorry for stealing the post; I've got a question regarding to Example 3 and 4 on Lecture 7.
How do you turn the Robin boundary conditions to a function of psi and phi?

[Victor Ivrii]

sorry for stealing the post; I've got a question regarding to Example 3 and 4 on Lecture 7.
How do you turn the Robin boundary conditions to a function of psi and phi?

It is not stealing but hijacking. Just plug $u=\phi(x+ct)+\psi (x-ct)$ into b.c. and you get a mixture of $\psi'(-ct)$, $\psi(-ct)$ and $\phi'(x+ct)$, $\phi(ct)$. But you know $\phi(ct)$ so you get 1-st order ODE for $\psi$.

[Shu Wang]

rofl, thanks alot.