Approximate diagonalization in differential systems and an effective algorithm for the computation of the spectral matrix

Abstract

1. IntroductionIn a recent paper [3], an extended Liouville–Green formulaformula herewas developed for solutions of the second-order differential equationformula hereHere γM(x) ∼Q−¼(x), QM(x) ∼Q−½(x) and εM(x)→0 as x→∞, while M([ges ]2) is an integer and γM and QM can be defined in terms of Q and its derivatives up to order M−1. The general form of (1·1) had been obtained previously by Cassell [5], [6], [7] and Eastham [10], [11, section 2·4]. In particular, the proof of (1·1) in [10] and [11] depended on the formulation of (1·2) as a first-order system and then on a process of M repeated diagonalization of the coefficient matrices in a sequence of related differential systems.

Locations

• Mathematical Proceedings of the Cambridge Philosophical Society - View
• arXiv (Cornell University) - View - PDF