Department of Mathematics
Texas A & M - Commerce
Student/Faculty Colloquium
Thursday, November 2, 2006
Henderson 302, 2:00pm
Hristo V. Kojouharov,
University of Texas - Arlington,
will speak on:
Qualitatively stable nonstandard finite difference methods for
dynamical systems in ecology
Abstract:
A new class of one-step nonstandard finite difference methods is
developed for first-order ordinary differential equations. The proposed
numerical techniques are based on a nonlocal modeling of the right-hand
side function and a nonstandard discretization of the time-derivative.
This approach leads to significant qualitative improvements in the
behavior of the numerical solution. For multi-dimensional autonomous
dynamical systems, positive and elementary-stable nonstandard finite
difference methods are formulated and analyzed, based on an extension
of the nonstandard discretization rules. Applications of the
nonstandard finite difference methods to specific biological systems
are also presented.