Applied Mathematics and Mathematical Physics Seminar

Abstract

Standard numerical integrators, such as the Runge-Kutta family of explicit finite-difference methods, are known to exhibit numerous scheme-dependent instabilities and generally fail to preserve some of the main essential qualitative features (such as positivity, boundedness, asymptotic stability, and bifurcation properties) of the governing continuous system they approximate. The talk will address the problem of designing appropriate discrete-time models that are dynamically consistent with the corresponding continuous-time model they approximate. Some models arising from modeling real-life phenomena in the natural and engineering sciences will be discussed.