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Volume 23, Issue 6
A Class of Two-Step Continuity Runge-Kutta Methods for Solving Singular Delay Differential Equations and Its Stability Analysis

Xin Leng, De-Gui Liu, Xiao-Qiu Song & Li-Rong Chen

J. Comp. Math., 23 (2005), pp. 647-656.

Published online: 2005-12

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  • Abstract

In this paper, a class of two-step continuity Runge-Kutta (TSCRK) methods for solving singular delay differential equations (DDEs) is presented. Analysis of numerical stability of the methods is given. We consider the two distinct cases: $(i)τ ≥ h$, $(ii)τ < h$, where the delay $τ$ and step size $h$ of the two-step continuity Runge-Kutta methods are both constant. The absolute stability regions of some methods are plotted and numerical examples show the efficiency of the method.

  • Keywords

Analysis of numerical stability, Singular delay differential equations, Two-step continuity Runge-Kutta methods.

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COPYRIGHT: © Global Science Press

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@Article{JCM-23-647, author = {Xin Leng, De-Gui Liu, Xiao-Qiu Song and Li-Rong Chen}, title = {A Class of Two-Step Continuity Runge-Kutta Methods for Solving Singular Delay Differential Equations and Its Stability Analysis}, journal = {Journal of Computational Mathematics}, year = {2005}, volume = {23}, number = {6}, pages = {647--656}, abstract = {

In this paper, a class of two-step continuity Runge-Kutta (TSCRK) methods for solving singular delay differential equations (DDEs) is presented. Analysis of numerical stability of the methods is given. We consider the two distinct cases: $(i)τ ≥ h$, $(ii)τ < h$, where the delay $τ$ and step size $h$ of the two-step continuity Runge-Kutta methods are both constant. The absolute stability regions of some methods are plotted and numerical examples show the efficiency of the method.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8844.html} }
TY - JOUR T1 - A Class of Two-Step Continuity Runge-Kutta Methods for Solving Singular Delay Differential Equations and Its Stability Analysis AU - Xin Leng, De-Gui Liu, Xiao-Qiu Song & Li-Rong Chen JO - Journal of Computational Mathematics VL - 6 SP - 647 EP - 656 PY - 2005 DA - 2005/12 SN - 23 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8844.html KW - Analysis of numerical stability, Singular delay differential equations, Two-step continuity Runge-Kutta methods. AB -

In this paper, a class of two-step continuity Runge-Kutta (TSCRK) methods for solving singular delay differential equations (DDEs) is presented. Analysis of numerical stability of the methods is given. We consider the two distinct cases: $(i)τ ≥ h$, $(ii)τ < h$, where the delay $τ$ and step size $h$ of the two-step continuity Runge-Kutta methods are both constant. The absolute stability regions of some methods are plotted and numerical examples show the efficiency of the method.

Xin Leng, De-Gui Liu, Xiao-Qiu Song and Li-Rong Chen. (2005). A Class of Two-Step Continuity Runge-Kutta Methods for Solving Singular Delay Differential Equations and Its Stability Analysis. Journal of Computational Mathematics. 23 (6). 647-656. doi:
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