On correct statement of singular BVPs for autonomous systems of nonlinear ODEs with the applications to hydrodynamics

Abstract

This paper deals with some autonomous systems (ASs) of nonlinear ordinary differential equations (ODEs) arising from incompressible fluid mechanics. For these systems defined on a (semi)infinite interval and having in a phase space an infinite set of pseudohyperbolic equilibrium points, we discuss an approach to correct statement of singular boundary value problems (BVPs) and their reduction to equivalent regular ones. The associated stable numerical methods are proposed and the results of their application are illustrated.