Approximating the basin of attraction of time-periodicODEs by meshless collocation
Peter Giesl, Holger Wendland · Discrete and Continuous Dynamical Systems · 2009
In this paper we study a periodic solution of ageneral time-periodic ordinary differential equation (ODE) anddetermine its basin of attraction usinga time-periodic Lyapunov function. We show the existence of a Lyapunovfunction satisfying a certain linear partial differential equation andapproximate it using meshless collocation.Therefore, we establish error estimates for the approximatereconstruction and collocation of functions $V(t,x)$ whichare periodic with respect to $t$.