Accurate approximated solution to the differential inclusion based on the ordinary differential equation

  • T. H. Nguyen Hanoi Univ. Industry, Vietnam
Keywords: Differential inclusion, differential equation, normal cone, projection

Abstract

UDC 517.9

Many problems in applied mathematics can be transformed and described by the differential inclusion $\dot x\in f(t, x)-N_Qx$ involving $N_Qx,$ which is a normal cone to a closed convex set $Q \in \mathbb R^n$ at $x\in Q.$ The Cauchy problem of this inclusion is studied in the paper. Since the change of $x$ leads to the change of $N_Qx,$ solving the inclusion becomes extremely complicated. In this paper, we consider an ordinary differential equation containing a control parameter $K.$ When $K$ 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 $K$) is proved in this paper.

 

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Published
22.01.2021
How to Cite
Nguyen, T. H. “Accurate Approximated Solution to the Differential Inclusion Based on the Ordinary Differential Equation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 73, no. 1, Jan. 2021, pp. 117 -27, doi:10.37863/umzh.v73i1.889.
Section
Research articles