Method for finding majorant function estimates required to determine Picard’s successive approximations convergence domain

Abstract

This paper deals with convergence of Picard’s successive approximations, which give a solution for perturbed body motion differential equations system through constructing a majorizing linear differential equation. The task is to determine the domain of used variables where these successive approximations converge and to estimate how large the error will be if we take a finite number of approximations. A method for finding majorant function estimates required to determine Picard’s successive approximations convergence domain is constructed.