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Volume 22, Issue 5
$\mathcal{H}$-Stability of Runge-Kutta Methods with Variable Stepsize for System of Pantograph Equations

Yang Xu, Jingjun Zhao & Mingzhu Liu

J. Comp. Math., 22 (2004), pp. 727-734.

Published online: 2004-10

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  • Abstract

This paper deals with $\mathcal{H}$-stability of Runge-Kutta methods with variable stepsize for the system of pantograph equations. It is shown that both Runge-Kutta methods with nonsingular matrix coefficient $A$ and stiffly accurate Runge-Kutta methods are $\mathcal{H}$-stable if and only if the modulus of stability function at infinity is less than 1.

  • Keywords

Delay differential equations, Stability, Runge-Kutta method.

  • AMS Subject Headings

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-727, author = {Xu , YangZhao , Jingjun and Liu , Mingzhu}, title = {$\mathcal{H}$-Stability of Runge-Kutta Methods with Variable Stepsize for System of Pantograph Equations}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {5}, pages = {727--734}, abstract = {

This paper deals with $\mathcal{H}$-stability of Runge-Kutta methods with variable stepsize for the system of pantograph equations. It is shown that both Runge-Kutta methods with nonsingular matrix coefficient $A$ and stiffly accurate Runge-Kutta methods are $\mathcal{H}$-stable if and only if the modulus of stability function at infinity is less than 1.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10299.html} }
TY - JOUR T1 - $\mathcal{H}$-Stability of Runge-Kutta Methods with Variable Stepsize for System of Pantograph Equations AU - Xu , Yang AU - Zhao , Jingjun AU - Liu , Mingzhu JO - Journal of Computational Mathematics VL - 5 SP - 727 EP - 734 PY - 2004 DA - 2004/10 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10299.html KW - Delay differential equations, Stability, Runge-Kutta method. AB -

This paper deals with $\mathcal{H}$-stability of Runge-Kutta methods with variable stepsize for the system of pantograph equations. It is shown that both Runge-Kutta methods with nonsingular matrix coefficient $A$ and stiffly accurate Runge-Kutta methods are $\mathcal{H}$-stable if and only if the modulus of stability function at infinity is less than 1.

Xu , YangZhao , Jingjun and Liu , Mingzhu. (2004). $\mathcal{H}$-Stability of Runge-Kutta Methods with Variable Stepsize for System of Pantograph Equations. Journal of Computational Mathematics. 22 (5). 727-734. doi:
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