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Volume 20, Issue 6
Nonlinear Stability of Natural Runge-Kutta Methods for Neutral Delay Differential Equations

Cheng-Jian Zhang

J. Comp. Math., 20 (2002), pp. 583-590.

Published online: 2002-12

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  • Abstract

This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonliner NDDEs, are given. In particular, it is shown thar the ($k,l$)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.

  • Keywords

Nonlinear stability, Neutral delay differential equations, Natural Runge-Kutta methods.

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COPYRIGHT: © Global Science Press

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@Article{JCM-20-583, author = {Zhang , Cheng-Jian}, title = {Nonlinear Stability of Natural Runge-Kutta Methods for Neutral Delay Differential Equations}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {6}, pages = {583--590}, abstract = {

This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonliner NDDEs, are given. In particular, it is shown thar the ($k,l$)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8943.html} }
TY - JOUR T1 - Nonlinear Stability of Natural Runge-Kutta Methods for Neutral Delay Differential Equations AU - Zhang , Cheng-Jian JO - Journal of Computational Mathematics VL - 6 SP - 583 EP - 590 PY - 2002 DA - 2002/12 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8943.html KW - Nonlinear stability, Neutral delay differential equations, Natural Runge-Kutta methods. AB -

This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonliner NDDEs, are given. In particular, it is shown thar the ($k,l$)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.

Zhang , Cheng-Jian. (2002). Nonlinear Stability of Natural Runge-Kutta Methods for Neutral Delay Differential Equations. Journal of Computational Mathematics. 20 (6). 583-590. doi:
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