Use of Shrink Wrapping for Interval Taylor Models in Algorithms of Computer-Assisted Proof of the Existence of Periodic Trajectories in Systems of Ordinary Differential Equations

Using interval Taylor models (TM), we construct algorithms for the computer-assisted proof of existence periodic trajectories in systems ordinary differential equations (ODEs). Although TMs allow one to guaranteed estimates families solutions ODEs when integrating over large time intervals, residual included begins grow exponentially and becomes dominant part estimate solution pencil, making it practically unusable. To eliminate this deficiency, creators TM—K. Makino M. Berz—proposed idea so-called “shrink wrapping.” We formalize original algorithm within framework TM definitions have adopted propose our own version wrapping,” more accurately adapted problem computer-aided trajectories.