Liu Bie Ju Centre for Mathematical Sciences
City University of Hong Kong
Mathematical Analysis and its Applications
Colloquium

Organized by Prof. Ya Yan LU and Prof. Wei Wei SUN

Numerical Analysis of Volterra Integral Equations

by

Professor Hermann Brunner
Memorial University of Newfoundland, Canada and
Hong Kong Baptist University, Hong Kong

Date: Jan 25, 2011 (Tuesday)
Time:4:30 pm to 5:30 pm
Venue: Room B6605 (College Conference Room)
Blue Zone, Level 6, Academic Building
City University of Hong Kong

ABSTRACT: In the first part of this talk I shall give a brief overview of the development of theory of Volterra integral equations, from Vito Volterra's fundamental 1896/1897 papers to recent (2010) results on the spectra of noncompact Volterra operators. This will be followed by a brief description of the 'state of the art' in the numerical analysis of Volterra integral equations, focusing on collocation methods in spaces of piecewise polynomials. While the optimal (super-) convergence properties of these methods are now well understood in the case of 'classical' Volterra integral equations, many key questions remain to be answered for equations with delay arguments and equations described by weakly singular, noncompact Volterra integral operators. In particular, the general convergence analysis for some of the first-kind integral equations originally studied by Volterra is still largely open. The talk will conclude with comments on current work and open problems.

** All interested are welcome **

For enquiry: 3442-9816