Discretization scheme in Volterra integro-differential equations that preserves stability and boundedness

Abstract

A nonstandard discretization scheme is applied to continuous Volterra integro-differential equations. We will show that under our discretization scheme the stability of the zero solution of the continuous dynamical system is preserved. Also, under the same discretization, using a combination of Lyapunov functionals, Laplace transforms and z-transforms, we show that the boundedness of solutions of the continuous dynamical system is preserved.

Keywords:

• Volterra integro-differential equations
• Discretization scheme
• Preserving Stability

AMS (2002) Subject Classifications:

• 39A10
• 34A97

Notes

^¶Email: [email protected]

Additional information

Notes on contributors

Eric R. Kaufmann

¶ ¶Email: [email protected]