Speaker: Dr. Kailash C. Patidar
Associate Professor
Department of Mathematics and Applied Mathematics
University of the Western Cape
Private Bag X17, 7535 Bellville, South Africa

Title: On the selection of non-standard finite difference modeling rules

Abstract: The non-standard finite difference methods are attracting many applied mathematicians. Because of their ease in construction, even engineers have started using them (see, e.g. K.C. Patidar, On the use of non-standard finite difference methods, Journal of Difference Equations and Applications, 11 (2005), 735-758; for such works). In this talk, we will consider a variety of ODEs and PDEs which involve one or more parameters. We discuss the role of these parameters and associated difficulties when these parameters take certain values. A number of numerical methods will then be discussed where the main emphasis will be on the role of some specific non-standard modeling rules.