Calculation of order ϵ dynamics for an NSFD discretization of a cube-root damped oscillator

Abstract

We determine an order ϵ solution to a discrete harmonic oscillator having cube-root damping. Comparison is made to the corresponding solution of the continuous differential equation model.

Keywords::

• finite difference methods
• asymptotic approximations
• nonlinear difference equations
• perturbation procedures

AMS Subject Classification::

• 34A34
• 39A10
• 41A60
• 65 L12
• 73D35

Acknowledgements

This work was supported in part by Faculty Development Funds from the School of Arts and Sciences, Clark Atlanta University. The author extends special thanks to Prof. 'Kale Oyedeji for many productive discussions on the subject of this study and for various editorial services related to this manuscript.