Existence and approximation for nonlinear dynamic equations using monotone iteration method

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 correspondsto a solution of the dynamic IVP on time scales. Under suitable conditions, we establish the uniform and monotonic convergence ofsequences to the extremal (minimal and maximal) solutions of the problem. The results provide a unified framework for analyzing dynamicequations on time scales via monotone iteration.