A shooting method is developed to approximate the eigenvalues and eigenfunctions of a 4th order Sturm-Liouville problem. The main tool is a miss-distance function M(), which counts the number ofâ€¦ (More)

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 (equallyâ€¦ (More)

We consider three numerical methods â€“ one based on power series, one on the Magnus series and matrix exponentials, and one a library initial value code â€“ for solving a linear system arising inâ€¦ (More)

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 integerâ€¦ (More)

Authorâ€™s address: Computational and Applied Mathematics Group, Royal Military College of Science, Shrivenham, Swindon Wilts SN6 8LA, U.K. Permission to copy without fee all or part of this materialâ€¦ (More)

In the setting of adjoint pairs of operators we consider the question: to what extent does the Weyl M -function see the same singularities as the resolvent of a certain restriction AB of the maximalâ€¦ (More)

This paper describes the algorithms and theory behind a new code for vector Sturm-Liouville problems. A new spectral function is defined for vector Sturm-Liouville problems; this is an integer valuedâ€¦ (More)

Spectral problems with band-gap spectral structure arise in numerous applications, including the study of crystalline structure and the determination of transmitted frequencies in photonicâ€¦ (More)

We show that for self-adjoint Jacobi matrices and SchrÃ¶dinger operators, peturbed by dissipative potentials in l(N) and L(0,âˆž) respectively, the finite section method does not omit any points of theâ€¦ (More)