Approximating local solution of an IVP of nonlinear first order ordinary hybrid differential equations

Approximating local solution of the IVPs of nonlinear hybrid differential equations

Abstract

In this paper, we prove a couple of approximation results for local existence and uniqueness of solution of an IVP of nonlinear first order ordinary hybrid differential equations under weaker Lipschitz condition by using the Dhage monotone iteration method based on a hybrid fixed point theorem of Dhage (2022) and Dhage {et al.} (2022). An approximation result for the Ulam-Hyers stability of the local solution of the considered hybrid differential equation is also established. Our main abstract results are also illustrated with a couple of numerical examples.