Numerical analysis for functional differential and integral equations

Abstract

From December 3–6, 2007, the Department of Mathematics at Hong Kong Baptist University hosted the International Workshop on Numerical Analysis and Computational Methods for Functional Differential and Integral Equations. This workshop, organized by Hermann Brunner of Memorial University of Newfoundland (Canada) & Hong Kong Baptist University, Leevan Ling and Tao Tang of Hong Kong Baptist University, and Chengjian Zhang of Huazhong University of Science and Technology (China) brought together some 40 members of research groups in Hong Kong, Taiwan and the mainland of China, Belgium, Canada, Japan, and Portugal. The aims of the workshop were twofold. First, it is to discuss recent and current work in this active area of numerical analysis/scientific computing. Second, it is to foster closer research contacts and research collaboration between participants. The eleven papers in this special issue of Frontiers of Mathematics in China reflect the broad spectrum of research work presented during the fourday workshop. Three of the papers are survey papers, dealing with theory and numerical analysis of nonlinear stiff Volterra functional differential equations (Li); collocation methods for pantograph-type delay differential and integral equations (Ishiwata and Muroya, note that Section 4 of the paper also contains some new research results); and current work and open problems in the numerical analysis of Volterra functional equations (Brunner). The study of various aspects of numerical stability for (continuous and discrete) delay problems is the focus of four papers: they are by Huang and Vandewalle (stability of Runge-Kutta-Pouset methods for Volterra integro-