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Modified Euler methods for differential inclusions. (English) Zbl 0788.34008
Kurzhanskii, Alexander B. (ed.) et al., Set-valued analysis and differential inclusions. A collection of papers resulting from a workshop held in Pamporovo, Bulgaria, September, 1990. Boston, MA: Birkhäuser. Prog. Syst. Control Theory. 16, 131-148 (1993).
Euler and modified Euler methods for numerical approximation of solutions of a differential inclusion \(x'(t) \in F(t,x(t))\) are discussed. The results concerning convergence of order 1 of Euler polygonal lines are given for upper semi-continuous convex valued \(F\) which satisfies a (strengthened) one-sided Lipschitz condition. Some numerical simulations are given.
For the entire collection see [Zbl 0782.00079].

34A60 Ordinary differential inclusions
49J24 Optimal control problems with differential inclusions (existence) (MSC2000)
65L05 Numerical methods for initial value problems involving ordinary differential equations