Quasilinearization method for an impulsive integro-differential system with delay

Bing Hu; Zhizhi Wang; Minbo Xu; Dingjiang Wang; Bing Hu; Zhizhi Wang; Minbo Xu; Dingjiang Wang

doi:10.3934/mbe.2022027

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 1: 612-623. doi: 10.3934/mbe.2022027

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Quasilinearization method for an impulsive integro-differential system with delay

Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China

Academic Editor: E. Oterkus

Received: 27 August 2021 Accepted: 19 October 2021 Published: 18 November 2021

In this paper, we obtain solution sequences converging uniformly and quadratically to extremal solutions of an impulsive integro-differential system with delay. The main tools are the method of quasilinearization and the monotone iterative. The results obtained are more general and applicable than previous studies, especially the quadratic convergence of the solution for a class of integro-differential equations, which have been involved little by now.
- impulsive integro-differential system,
- delay,
- quasilinearization,
- uniform convergence,
- quadratic convergence
Citation: Bing Hu, Zhizhi Wang, Minbo Xu, Dingjiang Wang. Quasilinearization method for an impulsive integro-differential system with delay[J]. Mathematical Biosciences and Engineering, 2022, 19(1): 612-623. doi: 10.3934/mbe.2022027

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Abstract

In this paper, we obtain solution sequences converging uniformly and quadratically to extremal solutions of an impulsive integro-differential system with delay. The main tools are the method of quasilinearization and the monotone iterative. The results obtained are more general and applicable than previous studies, especially the quadratic convergence of the solution for a class of integro-differential equations, which have been involved little by now.

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