A Unified Exhaustive Study Of Monotone Iterative Method For Initial Value Problems

Abstract

The method of upper, lower solutions, and coupled upper, lower solutions together with monotone iterative technique yields monotone sequences or alternating sequences, when the forcing function is the sum of two monotone functions. The sequences converge to extremal solutions or coupled extremal solutions of the nonlinear initial value problems. Furthermore, under uniqueness assumption the coupled extremal solutions converge to the unique solution of the nonlinear initial value problems.