Accurate approximated solution to the differential inclusion based on the ordinary differential equation
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...
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| Date: | 2021 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2021
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/889 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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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| DOI: | 10.37863/umzh.v73i1.889 |