Volume 19, Issue 2
The Stability of Linear Multistep Methods for Linear Systems of Neutral Differential Equations

Hong Jiong Tian, Jiao Xun Kuang & Lin Qiu

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J. Comp. Math., 19 (2001), pp.125-130

Published online: 2001-04

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  • Abstract

This paper deals with the numerical solution of initial value problems for systems of neutral differential equations y'(t)=f(t,y(t),y(t-tau),y'(t-tau)), t › 0, y(t) = phi(t) t‹ 0, where tau › 0, f and phi denote given vector-valued functions. The numerical stability of a linear multistep method is investigated by analysing the solution of the test equations y'(t)=Ay(t) + By(t-\tau) + Cy'(t-\tau), where A, B and C denote constant complex N \times N-matrices, and \tau › 0. We investigate the properties of adaptation of the linear multistep method and the characterization of the stability region. It is proved that the linear multistep method is NGP-stable if and only if its is A-stable for ordinary differential equations.

  • Keywords

Numerical stability Linear multistep method Delay differential equations

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@Article{JCM-19-125, author = {}, title = {The Stability of Linear Multistep Methods for Linear Systems of Neutral Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {2}, pages = {125--130}, abstract = { This paper deals with the numerical solution of initial value problems for systems of neutral differential equations y'(t)=f(t,y(t),y(t-tau),y'(t-tau)), t › 0, y(t) = phi(t) t‹ 0, where tau › 0, f and phi denote given vector-valued functions. The numerical stability of a linear multistep method is investigated by analysing the solution of the test equations y'(t)=Ay(t) + By(t-\tau) + Cy'(t-\tau), where A, B and C denote constant complex N \times N-matrices, and \tau › 0. We investigate the properties of adaptation of the linear multistep method and the characterization of the stability region. It is proved that the linear multistep method is NGP-stable if and only if its is A-stable for ordinary differential equations. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8963.html} }
TY - JOUR T1 - The Stability of Linear Multistep Methods for Linear Systems of Neutral Differential Equations JO - Journal of Computational Mathematics VL - 2 SP - 125 EP - 130 PY - 2001 DA - 2001/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8963.html KW - Numerical stability KW - Linear multistep method KW - Delay differential equations AB - This paper deals with the numerical solution of initial value problems for systems of neutral differential equations y'(t)=f(t,y(t),y(t-tau),y'(t-tau)), t › 0, y(t) = phi(t) t‹ 0, where tau › 0, f and phi denote given vector-valued functions. The numerical stability of a linear multistep method is investigated by analysing the solution of the test equations y'(t)=Ay(t) + By(t-\tau) + Cy'(t-\tau), where A, B and C denote constant complex N \times N-matrices, and \tau › 0. We investigate the properties of adaptation of the linear multistep method and the characterization of the stability region. It is proved that the linear multistep method is NGP-stable if and only if its is A-stable for ordinary differential equations.
Hong Jiong Tian, Jiao Xun Kuang & Lin Qiu. (1970). The Stability of Linear Multistep Methods for Linear Systems of Neutral Differential Equations. Journal of Computational Mathematics. 19 (2). 125-130. doi:
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