# zbMATH — the first resource for mathematics

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].

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