Volume 11, Issue 2
Convergence and Stability Analysis of Exponential General Linear Methods for Delay Differential Equations

Jingjun Zhao, Yu Li & Yang Xu

Numer. Math. Theor. Meth. Appl., 11 (2018), pp. 354-382.

Published online: 2018-11

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  • Abstract

In this paper, we study the convergence and stability properties of explicit exponential general linear methods for delay differential equations. We prove that, under some assumptions, for delay differential equations in Banach spaces, these numerical methods converge essentially with the order min {$P, Q+1$}, where $P$ and $Q$ denote the order and stage order of the methods for ordinary differential equations, respectively. By using an interpolation procedure for the delay term, we analyze the linear and nonlinear stability of exponential general linear methods for two classes of delay differential equations. The sufficient conditions on the stability of exponential general linear methods for the testing delay differential equations are provided. Several numerical experiments are given to demonstrate the conclusions.

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@Article{NMTMA-11-354, author = {}, title = {Convergence and Stability Analysis of Exponential General Linear Methods for Delay Differential Equations}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {11}, number = {2}, pages = {354--382}, abstract = {

In this paper, we study the convergence and stability properties of explicit exponential general linear methods for delay differential equations. We prove that, under some assumptions, for delay differential equations in Banach spaces, these numerical methods converge essentially with the order min {$P, Q+1$}, where $P$ and $Q$ denote the order and stage order of the methods for ordinary differential equations, respectively. By using an interpolation procedure for the delay term, we analyze the linear and nonlinear stability of exponential general linear methods for two classes of delay differential equations. The sufficient conditions on the stability of exponential general linear methods for the testing delay differential equations are provided. Several numerical experiments are given to demonstrate the conclusions.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0032}, url = {http://global-sci.org/intro/article_detail/nmtma/12434.html} }
TY - JOUR T1 - Convergence and Stability Analysis of Exponential General Linear Methods for Delay Differential Equations JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 354 EP - 382 PY - 2018 DA - 2018/11 SN - 11 DO - http://doi.org/10.4208/nmtma.OA-2017-0032 UR - https://global-sci.org/intro/article_detail/nmtma/12434.html KW - AB -

In this paper, we study the convergence and stability properties of explicit exponential general linear methods for delay differential equations. We prove that, under some assumptions, for delay differential equations in Banach spaces, these numerical methods converge essentially with the order min {$P, Q+1$}, where $P$ and $Q$ denote the order and stage order of the methods for ordinary differential equations, respectively. By using an interpolation procedure for the delay term, we analyze the linear and nonlinear stability of exponential general linear methods for two classes of delay differential equations. The sufficient conditions on the stability of exponential general linear methods for the testing delay differential equations are provided. Several numerical experiments are given to demonstrate the conclusions.

Jingjun Zhao, Yu Li & Yang Xu. (2020). Convergence and Stability Analysis of Exponential General Linear Methods for Delay Differential Equations. Numerical Mathematics: Theory, Methods and Applications. 11 (2). 354-382. doi:10.4208/nmtma.OA-2017-0032
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