Construction of reachable sets of controlled systems with second order of accuracy with respect to time step

The paper investigates the pixel method for constructing reachable sets of a dynamic controlled system. Sufficient conditions for a control system have been obtained under which the explicit second order Runge–Kutta method (a modified Euler method) provides the second order of accuracy with respect to a time step in constructing reachable sets, even if discontinuous functions are in the class of admissible controls.