American Institute of Mathematical Sciences

Advanced
May  2010, 13(3): 685-708. doi: 10.3934/dcdsb.2010.13.685

A Legendre-Gauss collocation method for nonlinear delay differential equations

Zhong-Qing Wang 1, and  Li-Lian Wang 2,

1. 

Department of Mathematics, Shanghai Normal University, Shanghai, 200234
2. 

Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371

Received  November 2008 Revised  October 2009 Published  February 2010

In this paper, we introduce an efficient Legendre-Gauss collocation method for solving nonlinear delay differential equations with variable delay. We analyze the convergence of the single-step and multi-domain versions of the proposed method, and show that the scheme enjoys high order accuracy and can be implemented in a stable and efficient manner. We also make numerical comparison with other methods.
Keywords: nonlinear delay differential equations, spectral accuracy., Legendre-Gauss collocation methods.
Mathematics Subject Classification: Primary: 5L60, 65L05, 65Q05, 41A1.
Citation: Zhong-Qing Wang, Li-Lian Wang. A Legendre-Gauss collocation method for nonlinear delay differential equations. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 685-708. doi: 10.3934/dcdsb.2010.13.685
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