Special Session 8: Differential, Difference, and Integral Equations: Techniques and Applications
NONSTANDARD DISCRETIZATION SCHEME IN VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS THAT PRESERVES UNIFORM ASYMPTOTIC STABILITY
Youssef N Raffoul
University of Dayton USA
Co-Author(s): SVETLIN G. GEORGIEV, Halis Can Koyuncuo\u{g}lu}, Marko Kosti\` c
Abstract:
We apply a nonstandard discretization scheme to continu-
ous Volterra integro-differential equations and we show that under this
discretization, the necessary and sufficient conditions for uniform as-
ymptotic stability of continuous Volterra integro-differential equations
are preserved. Our analysis is based on the notion of resolvent. An
example is provided as an application to our theory.