Approximating the basin of attraction of time-periodic ODEs by meshless collocation

In this paper we study a periodic solution of a general time-periodic ordinary differential equation (ODE) and determine its basin of attraction using a time-periodic Lyapunov function. We show the existence of a Lyapunov function satisfying a certain linear partial differential equation and approximate it using meshless collocation. Therefore, we establish error estimates for the approximate reconstruction and collocation of functions [V(t,x)] which are periodic with respect to [t] .