AN ALGORITHMIC APPROACH TO LOCAL SOLUTION OF THE NONLINEAR SECOND ORDER ORDINARY HYBRID INTEGRODIFFERENTIAL EQUATIONS
By
Janhavi B. Dhage, Shyam B. Dhage and Bapurao C. Dhage
Kasubai, Gurukul Colony, Thodga Road, Ahmedpur, Distr. Latur, Maharashtra, India-413515
Email: jbdhage@gmail.com, sbdhage4791@gmail.com, bcdhage@gmail.com
(Received: February 14, 20232; In format: February 22, 2023; Revised: April 29, 2023; Accepted: May 26, 2023)
DOI: https://doi.org/10.58250/jnanabha.2023.53133
Abstract
In this paper, we establish a couple of approximation results for local existence and uniqueness of the solution of an IVP of nonlinear second order ordinary hybrid integrodifferential equations by using the Dhage monotone iteration method based on the recent hybrid fixed point theorems of Dhage (2022) and Dhage et al. (2022). An approximation result for Ulam-Hyers stability of the local solution of the considered hybrid differential equation is also established. Finally, our main abstract results are also illustrated with a couple of numerical examples.
2020 Mathematical Sciences Classification: 34A12, 34A34, 34A45, 47H10
Keywords and Phrases: Ordinary differential equation; Dhage iteration method; Approximation theorems; Local existence and uniqueness; Ulam-Hyers stability.
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