Asymptotic solutions of the boundary value problems for the singularly perturbed differential algebraic equations with a turning point

TL;DR

This paper investigates boundary value problems for singularly perturbed differential-algebraic equations with turning points, establishing conditions for solution existence and uniqueness, and developing a method for constructing asymptotic solutions.

Contribution

It introduces new sufficient conditions for the existence and uniqueness of solutions and a novel technique for asymptotic solution construction in DAEs with turning points.

Findings

Established conditions for solution existence and uniqueness

Developed a technique for asymptotic solutions

Analyzed boundary value problems with turning points

Abstract

This paper deals with the boundary value problems for the singularly perturbed differential-algebraic system of equations. The case of turning points has been studied. The sufficient conditions for existence and uniqueness of the solution of the boundary value problems for DAEs have been found. The technique of constructing the asymptotic solutions has been developed