Rocky Mountain Journal of Mathematics

Asymptotic behavior of a planar dynamic system

Gro Hovhannisyan

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Abstract

We investigate the asymptotic solutions of the planar dynamic systems and the second order equations on a time scale by using a new version of Levinson's asymptotic theorem. In this version the error estimate is given in terms of the characteristic (Riccati) functions which are constructed from the phase functions of an asymptotic solution. It means that the improvement of the approximation depends essentially on the asymptotic behavior of the Riccati functions. We describe many different approximations using the flexibility of this approach. As an application we derive the analogue of D'Alembert's formula for the one dimensional wave equation in a discrete time.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 4 (2014), 1203-1242.

Dates
First available in Project Euclid: 31 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1414760950

Digital Object Identifier
doi:10.1216/RMJ-2014-44-4-1203

Mathematical Reviews number (MathSciNet)
MR3274345

Zentralblatt MATH identifier
1307.34136

Subjects
Primary: 34E10: Perturbations, asymptotics 39A10: Difference equations, additive

Keywords
Dynamic systems on a time scale asymptotic solutions characteristic function Riccati equation perturbation method

Citation

Hovhannisyan, Gro. Asymptotic behavior of a planar dynamic system. Rocky Mountain J. Math. 44 (2014), no. 4, 1203--1242. doi:10.1216/RMJ-2014-44-4-1203. https://projecteuclid.org/euclid.rmjm/1414760950


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