# American Institute of Mathematical Sciences

December  2009, 25(4): 1249-1274. doi: 10.3934/dcds.2009.25.1249

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

 1 Department of Mathematics, University of Sussex, Brighton, BN1 9RF, United Kingdom, United Kingdom

Received  November 2007 Revised  May 2009 Published  September 2009

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 $t$.
Citation: Peter Giesl, Holger Wendland. Approximating the basin of attraction of time-periodic ODEs by meshless collocation. Discrete & Continuous Dynamical Systems, 2009, 25 (4) : 1249-1274. doi: 10.3934/dcds.2009.25.1249
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