Approximating of unstable cycle in nonlinear autonomous systems

Numerical procedures for approximate construction of cycles in nonlinear systems are studied. The procedures are based on functional parameter methods combined with mechanical quadratures, Newton's, and gradient methods. The convergence rate of the procedures is studied, as well as their range of applicability, and their stability with respect to small perturbations of the parameters. The results obtained can be applied to nonlinear problems described by ordinary differential equations, to the systems with delay, and to distributed systems.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Periodic solutions of autonomous systems under discretization

The existence of a sequence of periodic trajectories of a general one-step numerical scheme corresponding to a null sequence of constant time-steps is established under the assumption that the autonomous ordinary differential equation has an isolated periodic solution with non-zero topological index. The convergence of the linearly interpolated numerical curve to the original invariant curve with respect to the Hausdorff metric is also shown. (orig.)Available from TIB Hannover: RR 5549(327)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman