Nonlinear Stability and D-Convergence of Additive Runge-Kutta Methods for Multidelay-Integro-Differential Equations
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 multidelay-integro-differential equations (MDIDEs). GDN-stability and D-convergence are introduced and proved. It is shown that...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/854517 |
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| _version_ | 1849685604127735808 |
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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 multidelay-integro-differential equations (MDIDEs). 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. A numerical example is given to illustrate the theoretical results. |
| format | Article |
| id | doaj-art-c4e5284481e8421ab5a7fc8382d8bfff |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c4e5284481e8421ab5a7fc8382d8bfff2025-08-20T03:23:03ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/854517854517Nonlinear Stability and D-Convergence of Additive Runge-Kutta Methods for Multidelay-Integro-Differential EquationsHaiyan 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 multidelay-integro-differential equations (MDIDEs). 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. A numerical example is given to illustrate the theoretical results.http://dx.doi.org/10.1155/2012/854517 |
| spellingShingle | Haiyan Yuan Jingjun Zhao Yang Xu Nonlinear Stability and D-Convergence of Additive Runge-Kutta Methods for Multidelay-Integro-Differential Equations Abstract and Applied Analysis |
| title | Nonlinear Stability and D-Convergence of Additive Runge-Kutta Methods for Multidelay-Integro-Differential Equations |
| title_full | Nonlinear Stability and D-Convergence of Additive Runge-Kutta Methods for Multidelay-Integro-Differential Equations |
| title_fullStr | Nonlinear Stability and D-Convergence of Additive Runge-Kutta Methods for Multidelay-Integro-Differential Equations |
| title_full_unstemmed | Nonlinear Stability and D-Convergence of Additive Runge-Kutta Methods for Multidelay-Integro-Differential Equations |
| title_short | Nonlinear Stability and D-Convergence of Additive Runge-Kutta Methods for Multidelay-Integro-Differential Equations |
| title_sort | nonlinear stability and d convergence of additive runge kutta methods for multidelay integro differential equations |
| url | http://dx.doi.org/10.1155/2012/854517 |
| work_keys_str_mv | AT haiyanyuan nonlinearstabilityanddconvergenceofadditiverungekuttamethodsformultidelayintegrodifferentialequations AT jingjunzhao nonlinearstabilityanddconvergenceofadditiverungekuttamethodsformultidelayintegrodifferentialequations AT yangxu nonlinearstabilityanddconvergenceofadditiverungekuttamethodsformultidelayintegrodifferentialequations |