Volume 18, Issue 2
D-Convergence and Stability of a Class of Linear Multistep Methods for Nonlinear DDEs

J. Comp. Math., 18 (2000), pp. 199-206.

Published online: 2000-04

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• Abstract

This paper deals with the error behaviour and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation (LMLMs) as applied to the nonlinear delay differential equations (DDEs). It is showtn that a LMLM is generally stable with respect to the problem of class $D_{σγ}$, and a p-order linear multistep method together with a q-order Lagrangian interpolation leads to a D-convergent LMLM of order min {$p,q+1$}.

• Keywords

D-Convergence, Stability, Multistep methods, Nonlinear DDEs.

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@Article{JCM-18-199, author = {Cheng-Jia Zhang , and Xiao-Xin Liao , }, title = {D-Convergence and Stability of a Class of Linear Multistep Methods for Nonlinear DDEs}, journal = {Journal of Computational Mathematics}, year = {2000}, volume = {18}, number = {2}, pages = {199--206}, abstract = {

This paper deals with the error behaviour and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation (LMLMs) as applied to the nonlinear delay differential equations (DDEs). It is showtn that a LMLM is generally stable with respect to the problem of class $D_{σγ}$, and a p-order linear multistep method together with a q-order Lagrangian interpolation leads to a D-convergent LMLM of order min {$p,q+1$}.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9035.html} }
TY - JOUR T1 - D-Convergence and Stability of a Class of Linear Multistep Methods for Nonlinear DDEs AU - Cheng-Jia Zhang , AU - Xiao-Xin Liao , JO - Journal of Computational Mathematics VL - 2 SP - 199 EP - 206 PY - 2000 DA - 2000/04 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9035.html KW - D-Convergence, Stability, Multistep methods, Nonlinear DDEs. AB -

This paper deals with the error behaviour and the stability analysis of a class of linear multistep methods with the Lagrangian interpolation (LMLMs) as applied to the nonlinear delay differential equations (DDEs). It is showtn that a LMLM is generally stable with respect to the problem of class $D_{σγ}$, and a p-order linear multistep method together with a q-order Lagrangian interpolation leads to a D-convergent LMLM of order min {$p,q+1$}.

Cheng-Jia Zhang & Xiao-Xin Liao. (1970). D-Convergence and Stability of a Class of Linear Multistep Methods for Nonlinear DDEs. Journal of Computational Mathematics. 18 (2). 199-206. doi:
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