Accurate approximated solution to the differential inclusion based on the ordinary differential equation
DOI:
https://doi.org/10.37863/umzh.v73i1.889Keywords:
Differential inclusion, differential equation, normal cone, projectionAbstract
UDC 517.9
Many problems in applied mathematics can be transformed and described by the differential inclusion ˙x∈f(t,x)−NQx involving NQx, which is a normal cone to a closed convex set Q∈Rn at x∈Q. The Cauchy problem of this inclusion is studied in the paper. Since the change of x leads to the change of NQx, 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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