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Article Contents

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

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