Stability analysis of block boundary value methods for the neutral differential equation with many delays

Yang Xu; Jingjun Zhao; Zheng Gao

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Stability analysis of block boundary value methods for the neutral differential equation with many delays

机译：中立型时滞微分方程的块边值方法稳定性分析

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摘要

This paper mainly deals with the asymptotic stability properties of block boundary value methods (B_2VMs) for the neutral differential equation with many delays. For the time lagging arguments, a technique of Lagrange interpolation is considered. Under some certain conditions, it is proved that B_2VMs can preserve the asymptotic stability of exact solutions for the neutral differential equation with many delays if and only if B_2VMs are A-stable for ordinary differential equation. Moreover, some numerical experiments are given to confirm the main conclusion.

机译：本文主要研究具有许多时滞的中立型微分方程的块边界值方法（B_2VMs）的渐近稳定性。对于时滞参数，考虑使用Lagrange插值技术。在某些特定条件下，证明了，当且仅当B_2VM对常微分方程是A稳定的时，B_2VM才能保持中立微分方程精确解的渐近稳定性。此外，通过一些数值实验来证实主要结论。

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来源
《Applied Mathematical Modelling》 |2014年第1期|325-335|共11页
作者
Yang Xu; Jingjun Zhao; Zheng Gao;
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作者单位

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China;

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China;

Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Neutral differential equation; Block boundary value methods; Asymptotic stability;

机译：中立型微分方程;块边界值法;渐近稳定性;

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2. An analysis of delay-dependent stability of symmetric boundary value methods for the linear neutral delay integro-differential equations with four parameters [J] . Jingjun Zhao, Yan Fan, Yang Xu Applied Mathematical Modelling . 2015,第9期

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3. Delay-dependent stability analysis of Runge-Kutta methods for neutral delay differential equations [J] . 哈尔滨工业大学学报（英文版） . 2002,第002期

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5. Numerical solution of retarded and neutral delay differential equations using continuous Runge-Kutta methods. [D] . Hayashi, Hiroshi. 1996

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6. Stability analysis of a state-dependent delay differential equation for cell maturation: analytical and numerical methods [O] . Philipp Getto, Mats Gyllenberg, Yukihiko Nakata, -1

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7. INSTABILITY ANALYSIS OF NONLINEAR NEUTRAL DIFFERENTIAL DIFFERENCE SYSTEMS WITH INFINITE DELAYS(The Functional and Algebraic Method for Differential Equations) [O] . Ma W.B., Takeuchi Y. 1996

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8. New Stability Results for Runge-Kutta Methods Adapted to Delay Differential211 Equations [R] . Van den Heuvel, E. G. 1998

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Stability analysis of block boundary value methods for the neutral differential equation with many delays

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