Existence and approximation for nonlinear dynamic equations using monotone iteration method

Year 2025, Volume: 2 Issue: 2, 31 - 36, 31.07.2025

Nour Alsharif

Abstract

This paper improves a generalized monotone iterative technique for solving dynamic initial value problems (IVPs) on time scales,
using the method of coupled lower and upper solutions. We construct monotone sequences of iterates, each of which corresponds
to a solution of the dynamic IVP on time scales. Under suitable conditions, we establish the uniform and monotonic convergence of
sequences to the extremal (minimal and maximal) solutions of the problem. The results provide a unified framework for analyzing dynamic
equations on time scales via monotone iteration.

Keywords

Comparison results, Monotone iterative technique, Coupled upper and lower solutions

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