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Accurate Approximating Solution of the Differential Inclusion Based on the Ordinary Differential Equation
- Source :
- Ukrainian Mathematical Journal. 73:131-143
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
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.
Details
- ISSN :
- 15739376 and 00415995
- Volume :
- 73
- Database :
- OpenAIRE
- Journal :
- Ukrainian Mathematical Journal
- Accession number :
- edsair.doi...........dbd75ddde32fa938ededb8121a1a9ffa