This paper gives the analysis and numerics underlying a shooting method for approximating the eigenvalues of nonselfadjoint Sturm-Liouville problems. We consider even order problems with (equally divided) separated boundary conditions. The method can nd the eigenvalues in a rectangle and in a left half-plane. It combines the argument principle with the… (More)
The performance of Algorithm 700 is reviewed on a number of test problems, highlighting the strengths and weaknesses of the SLEIGN code.
We describe a new code (SLEUTH) for numerical solution of regular two-point fourth-order Sturm-Liouvlle eigenvalue problems. Eigenvalues are computed according to index: the user specifies an integer <italic>k</italic>***0, and the code computes an approximation to the <italic>k</italic>th eigenvalue. Eigenfunctions are also avialable through an auxiliary… (More)
In this paper, we confirm, with absolute certainty, a conjecture on a certain oscillatory behaviour of higher auto-ionizing resonances of atoms and molecules beyond a threshold. These results not only definitely settle a more than 30 year old controversy in Rittby et al. but also provide new and reliable information on the threshold. Our… (More)
We present a rigorous analysis of the performance of some one-step discretization schemes for a class of PT-symmetric singular boundary eigenvalue problem which encompasses a number of different problems whose investigation has been inspired by the 2003 article of Benilov et al. (J Fluid Mech 497:201–224, 2003). These discretization schemes are analyzed as… (More)