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

Abstract

In this paper, we establish a couple of approximation results for local existence and uniqueness of the solution of a IVP of nonlinear second order ordinary hybrid differential  equations with maxima under weaker partial compactness and partial Lipschitz type conditions 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 with maxima is also established. Finally, our main abstract results are also illustrated with a couple of numerical examples.