Approximating  the basin of attraction of time-periodicODEs by meshless collocation

Peter Giesl; Holger Wendland

doi:10.3934/dcds.2009.25.1249

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2009, Volume 25, Issue 4: 1249-1274. Doi: 10.3934/dcds.2009.25.1249

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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

Received: November 2007

Revised: May 2009

Published: December 2009

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Abstract

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 $t$.

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Mathematics Subject Classification: Primary: 37C55, 65N35; Secondary: 34C25, 65N15.

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