I am trying to find the eigenvalues and eigenvectors of the Laplacian with mixed boundary conditions on $[0,L]$:
More precisely:
$$X''(x) = \lambda X(x)$$ with $X'(0)=0$ and $X(L)=a$.
I know how to do it with pure Dirichlet or pure Neumann, but not for this mixture.
Could you help me or point me to the right reference ?
Thanks folk
Just found part of the answer here: http://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors_of_the_second_derivative#Mixed_Dirichlet-Neumann_boundary_conditions
but I am not sure how to relate it to parameter $a$ in the question.
any help welcome