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AIP Conf. Proc. / Volume 1067 / Issue 1

Compatible Discretizations for Continuous Dynamical Systems

AIP Conf. Proc. -- October 30, 2008 -- Volume 1067, pp. 28-37
APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS: Proceedings of the 34th Conference on Applications of Mathematics in Engineering and Economics (AMEE '08); doi:10.1063/1.3030798

Issue Date: 30 October 2008

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ABSTRACT

H. V. Kojouharov^a and D. T. Dimitrov^b
^aDept. of Mathematics, The University of Texas at Arlington P.O. Box 19408, Arlington, TX 76019-0408, USA
^bStatistical Center for HIV/AIDS Research and Prevention (SCHARP) Vaccine & Infectious Disease Institute, Fred Hutchinson Cancer Research Center Seattle, WA 98109-1024, USA

Inthis paper, we briefly review the history of the nonstandardfinite difference (NSFD) methods and their application to a widerange of physical and biological problems. Emphasis is given onthe use of the nonstandard discretization ideas to the numericalsolution of continuous dynamical systems. In that context, specific examplesof positive and elementary stable nonstandard (PESN) finite difference schemesare presented. We also outline possible future research directions forthe construction of structural property-preserving numerical methods and discuss someopen problems in the general area of nonstandard discretizations ofdifferential equations. ©2008 American Institute of Physics

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