Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays
This paper is devoted to the stability and convergence analysis of the additive Runge-Kutta methods with the Lagrangian interpolation (ARKLMs) for the numerical solution of a delay differential equation with many delays. GDN stability and D-Convergence are introduced and proved. It is shown that str...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/456814 |
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| _version_ | 1832546552704401408 |
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| author | Haiyan Yuan Jingjun Zhao Yang Xu |
| author_facet | Haiyan Yuan Jingjun Zhao Yang Xu |
| author_sort | Haiyan Yuan |
| collection | DOAJ |
| description | This paper is devoted to the stability and convergence analysis of the additive Runge-Kutta methods with the Lagrangian interpolation (ARKLMs) for the numerical solution of a delay differential equation with many delays. GDN stability and D-Convergence are introduced and proved. It is shown that strongly algebraically stability gives D-Convergence DA, DAS, and ASI stability give GDN stability. Some examples are given in the end of this paper which confirms our results. |
| format | Article |
| id | doaj-art-acd107f9d7834516b4da8a1b2a63eef8 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-acd107f9d7834516b4da8a1b2a63eef82025-02-03T06:48:17ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/456814456814Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many DelaysHaiyan Yuan0Jingjun Zhao1Yang Xu2Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaThis paper is devoted to the stability and convergence analysis of the additive Runge-Kutta methods with the Lagrangian interpolation (ARKLMs) for the numerical solution of a delay differential equation with many delays. GDN stability and D-Convergence are introduced and proved. It is shown that strongly algebraically stability gives D-Convergence DA, DAS, and ASI stability give GDN stability. Some examples are given in the end of this paper which confirms our results.http://dx.doi.org/10.1155/2012/456814 |
| spellingShingle | Haiyan Yuan Jingjun Zhao Yang Xu Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays Journal of Applied Mathematics |
| title | Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays |
| title_full | Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays |
| title_fullStr | Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays |
| title_full_unstemmed | Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays |
| title_short | Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays |
| title_sort | some stability and convergence of additive runge kutta methods for delay differential equations with many delays |
| url | http://dx.doi.org/10.1155/2012/456814 |
| work_keys_str_mv | AT haiyanyuan somestabilityandconvergenceofadditiverungekuttamethodsfordelaydifferentialequationswithmanydelays AT jingjunzhao somestabilityandconvergenceofadditiverungekuttamethodsfordelaydifferentialequationswithmanydelays AT yangxu somestabilityandconvergenceofadditiverungekuttamethodsfordelaydifferentialequationswithmanydelays |