Stability of a class of matrices with applications to absorbing boundary conditions for Schrödinger-type equations Original Research Article

In this paper, the stability of a class of complex matrices with a certain structure is studied; that is, conditions are obtained that ensure that all the eigenvalues of these matrices have a negative real part. This general result is used to prove the stability of the matrix obtained when the method of lines is considered to discretize in space a Schrödinger-type equation along with certain absorbing boundary conditions developed recently in the literature [1].