Details of Grant 

EPSRC Reference:	GR/K17750/01
Title:	THEORETICAL & NUMERICAL APPROACH TO SPECTRAL ANALYSIS FOR STURM-LIOUVILLE PROBLEMS
Principal Investigator:	Pearson, Professor D
Other Investigators:	Price, Dr JD
Researcher Co-Investigators:
Project Partners:
Department:	Applied Mathematics
Organisation:	University of Hull
Scheme:	Standard Research (Pre-FEC)
Starts:	01 October 1994	Ends:	30 September 1997	Value (£):	92,770
EPSRC Research Topic Classifications:	Numerical Analysis
EPSRC Industrial Sector Classifications:
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Panel History:
Summary on Grant Application Form
Collaborative research is proposed by Professor Pearson with Dr J D Pryce, assisted by two research assistants and with the participation of Dr J P Killingbeck, on the spectral analysis of the Schrdinger equation and other Sturm-Liouville differential equations with their discrete analogues.New theoretical and computational approaches will be developed for the analysis of both discrete and singular spectra. A new numerical approach to singular SL problems will be implemented, depending on the Gilbert/Pearson notion of subordinacy and making use of Pryce's NAG algorithms. A recently formulated asymptotic condition, analogous to subordinacy, but applicable to absolutely continuous spectra, will underpin a new numerical approach to the analysis of continuous spectra. Value distribution methods stemming from under a previous SERC grant will be adapted for use at fixed spectral parameter and applied to the study of the Weyl m-function. Recent work on matrix operators in infinite dimensions is expected to throw new light on the discretisation of continuous Schrdinger problems.Other proposed investigations may include: a study of the dependence on energy of the error for finite difference methods, the relationship between matrix shooting methods and matrix eigenvalue formulation of discrete spectral problems in finite difference form. Among outcomes of the research will be the creation and implementation of new algorithms for singular Sturm-Liouville problems, particularly on the continuous part of the spectrum.
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Organisation Website:	http://www.hull.ac.uk