Dhage iteration method for an algorithmic approach to local solution of the nonlinear second order ordinary hybrid differential equations
Dhage, B., Dhage, J., Dhage, S. (2023). Dhage iteration method for an algorithmic approach to local solution of the nonlinear second order ordinary hybrid differential equations. EKB Journal Management System, 11(2), 1-10. doi: 10.21608/ejmaa.2023.191335.1008
Bapurao C. Dhage; Janhavi B. Dhage; Shyam B. Dhage. "Dhage iteration method for an algorithmic approach to local solution of the nonlinear second order ordinary hybrid differential equations". EKB Journal Management System, 11, 2, 2023, 1-10. doi: 10.21608/ejmaa.2023.191335.1008
Dhage, B., Dhage, J., Dhage, S. (2023). 'Dhage iteration method for an algorithmic approach to local solution of the nonlinear second order ordinary hybrid differential equations', EKB Journal Management System, 11(2), pp. 1-10. doi: 10.21608/ejmaa.2023.191335.1008
Dhage, B., Dhage, J., Dhage, S. Dhage iteration method for an algorithmic approach to local solution of the nonlinear second order ordinary hybrid differential equations. EKB Journal Management System, 2023; 11(2): 1-10. doi: 10.21608/ejmaa.2023.191335.1008

Dhage iteration method for an algorithmic approach to local solution of the nonlinear second order ordinary hybrid differential equations

Electronic Journal of Mathematical Analysis and Applications
Volume 11, Issue 2, July 2023, Page 1-10  XML PDF (461.22 K)
Document Type: Regular research papers
DOI: 10.21608/ejmaa.2023.191335.1008
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Authors
Bapurao C. Dhage email orcid 1; Janhavi B. Dhage2; Shyam B. Dhage2
1"Kasubai", Gurukul Colony, Ahmedpur-413 515, Dist.: Latur, Maharashtra, India
2Kasubai Gurukul Colony,Ahmedpur
Abstract
It is known that the Dhage iteration method is very much useful for proving the existence and approximation results for nonlinear hybrid differential and integral equations.
In this paper, we introduce a notion of the local solution for the initial value problems of nonlinear second order ordinary differential equations and establish a couple of approximation results for local existence and uniqueness of the solution via Dhage monotone iteration method. Again, various hybrid fixed point theorems are involved in the Dhage iteration method as per the demand of the nonlinear hybrid equations. Here, we base our Dhage monotone iteration method on the recent hybrid fixed point theorems of Dhage (2022) and Dhage {\em et al.} (2022).
There are different notions of stability of the nonlinear equations. Here we discuss the Ulam-Hyers stability of the local solution of the considered hybrid differential equation is also established by construction of an algorithm. Finally, our main abstract results are also illustrated with a couple of numerical examples.
There are different notions of stability of the nonlinear nonlinear equations. Here we discuss the Ulam-Hyers stability of the local solution of the considered hybrid differential equation is also established by construction of an algorithm. Finally, our main abstract results are also illustrated with a couple of numerical examples.
Keywords
Ordinary differential equation; Hybrid fixed point principle; Dhage iteration method; Approximation theorems., Ulam-Hyers stability
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