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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Main Authors: Haiyan Yuan, Jingjun Zhao, Yang Xu
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/854517
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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.
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institution DOAJ
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language English
publishDate 2012-01-01
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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