Open AccessAccurate approximated solution to the differential inclusion based on the ordinary differential equation
Author(s) -
Thanh-Hung Nguyen
Publication year - 2021
Publication title -
ukraïnsʹkij matematičnij žurnal
Language(s) - English
Resource type - Journals
ISSN - 1027-3190
DOI - 10.37863/umzh.v73i1.889
Subject(s) - differential inclusion , mathematics , ordinary differential equation , inclusion (mineral) , exact differential equation , regular polygon , mathematical analysis , differential equation , cauchy distribution , set (abstract data type) , initial value problem , computer science , physics , geometry , thermodynamics , programming language
UDC 517.9Many problems in applied mathematics can be transformed and described by the differential inclusion involving which is a normal cone to a closed convex set at The Cauchy problem of this inclusion is studied in the paper. Since the change of leads to the change of solving the inclusion becomes extremely complicated. In this paper, we consider an ordinary differential equation containing a control parameter When is large enough, the studied equation gives a solution approximating to a solution of the inclusion above. The theorem about the approximation of these solutions with arbitrary small error (this error can be controlled by increasing ) is proved in this paper.