High precision methods in eigenvalue problems and their applications

Akulenko's work gathers together the main ways of computing eigenvalues, covering closed-form analytical techniques, asymptotic expansions, numerical schemes, and hybrids of these approaches. A substantial part is devoted to a newly developed technique that speeds up convergence for Sturm-Liouville problems. Boundary-value problems with first, second, and third kind conditions are examined alongside it.

The volume also introduces high-precision asymptotic procedures for locating eigenvalues and eigenfunctions associated with higher oscillation modes. To show how widely these tools apply, the author works through many eigenvalue problems drawn from oscillation theory, acoustics, elasticity, hydrodynamics, geophysics, quantum mechanics, structural mechanics, electrodynamics, and microelectronics.