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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

Peter Giesl 1, and  Holger Wendland 1,

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 $t$.
Keywords: radial basis function., partial differential equation, periodic orbit, periodic differential equation, meshless collocation, Lyapunov function, basin of attraction.
Mathematics Subject Classification: Primary: 37C55, 65N35; Secondary: 34C25, 65N1.
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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