Numerical-analytic successive approximation method for the investigation of periodic solutions of nonlinear integro-differential systems with piecewise constant argument of generalized type

Year 2024, Volume: 53 Issue: 5, 1272 - 1290, 15.10.2024

Kuo-shou Chiu

https://doi.org/10.15672/hujms.1298168

Abstract

In this paper, we focus on investigating the existence and approximation of periodic solutions for a nonlinear integro-differential system with a piecewise alternately advanced and retarded argument of generalized type, referred to as DEPCAG. The argument is a general step function, and we obtain criteria for the existence of periodic solutions for such equations. Our approach involves converting the given DEPCAG into an equivalent integral equation and using a new approach for periodic solutions. We construct appropriate mappings and employ a numerical-analytic method to investigate periodic solutions of the ordinary differential equation given by A. M. Samoilenko [32]. Additionally, we use the contraction mapping principle to demonstrate the existence of a unique periodic solution.

Keywords

numerical-analytic method, piecewise constant argument of generalized type, convergence of approximate solutions, periodic solutions, hybrid equations

Supporting Institution

Universidad Metropolitana de Ciencias de la Educación

Project Number

FONDECYT 1231256 and DIUMCE 09-2023-SAC.

Thanks

The research was supported by FONDECYT 1231256 and DIUMCE 09-2023-SAC.

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