Discrete Approximation of Impulsive Differential Inclusions

The article deals with the approximation of the solution set and the reachable sets of an impulsive differential inclusion with variable times of impulses. It is strongly connected to 11 T. Donchev ( 2008 ). Approximation of the solution set of impulsive systems . In Lecture Notes in Comput. Sci . ( et al. . eds.). Vol. 4818 , Springer-Verlag , Berlin , pp. 309 – 316 . Google Scholar]] and is its continuation. We achieve order of convergence 1 for the Euler approximation under Lipschitz assumptions on the set-valued right-hand side and on the functions describing the jump surfaces and jumps themselves. Another criterion prevents the beating phenomena and generalizes available conditions. Several test examples illustrate the conditions and the practical evaluation of the jump conditions.