A Legendre-Gauss collocation method for nonlinear delaydifferential equations

Zhong-Qing Wang; Li-Lian Wang

doi:10.3934/dcdsb.2010.13.685

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2010, Volume 13, Issue 3: 685-708. Doi: 10.3934/dcdsb.2010.13.685

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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: October 31, 2008

Revised: September 30, 2009

Published: September 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 5L60, 65L05, 65Q05, 41A10.

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