显式和对角隐式Rung-Kutta方法求解中立型泛函微分方程的非线性稳定性

doi:10.12288/szjs.2011.1.8

数值计算与计算机应用 ›› 2011, Vol. 32 ›› Issue (1): 8-22.DOI: 10.12288/szjs.2011.1.8

显式和对角隐式Rung-Kutta方法求解中立型泛函微分方程的非线性稳定性

苏凯^1,2, 王锦红¹, 张宏伟¹, 王晚生¹

1. 长沙理工大学数学与计算科学学院, 长沙 410114;
2. 湘潭大学数学与计算科学学院, 湖南湘潭 411105

收稿日期:2009-07-12 出版日期:2011-03-15 发布日期:2011-03-08
基金资助:
国家自然科学基金(11001033, 10871164)、湖南省自然科学基金(10JJ4003)、湖南省教育厅(08C121)资助科研项目及电力青年科技创新资助项目.

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苏凯, 王锦红, 张宏伟, 王晚生. 显式和对角隐式Rung-Kutta方法求解中立型泛函微分方程的非线性稳定性[J]. 数值计算与计算机应用, 2011, 32(1): 8-22.

Su Kai, Wang Jinhong, Zhang Hongwei, Wang Wansheng. NONLINEAR STABILITY OF EXPLICIT AND DIAGONALLY IMPLICIT RUNGE-KUTTA METHODS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS[J]. Journal of Numerical Methods and Computer Applications, 2011, 32(1): 8-22.

NONLINEAR STABILITY OF EXPLICIT AND DIAGONALLY IMPLICIT RUNGE-KUTTA METHODS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

Su Kai^1,2, Wang Jinhong¹, Zhang Hongwei¹, Wang Wansheng¹

1. School of Mathematics and Computational Science, Changsha University of Science and Technology, Changsha 410114, China;
2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China

Received:2009-07-12 Online:2011-03-15 Published:2011-03-08

本文致力于研究巴拿赫空间中非线性中立型泛函微分方程显式和对角隐式Rung-Kutta方法的稳定性.获得了一些显式和对角隐式Rung-Kutta方法求解非线性中立型泛函微分方程的数值稳定性和条件收缩性结果,数值试验验证了这些结果.

关键词： 显式和对角隐式Rung-Kutta方法, 中立型泛函微分方程, 巴拿赫空间, 非线性稳定性

This paper is concerned with the stability of explicit and diagonally implicit Runge-Kutta methods for nonlinear neutral functional differential equations (NFDEs) in Banach spaces. The results on the numerical stability and conditional contractivity of some explicit and diagonally implicit Runge-Kutta methods for nonlinear NFDEs are obtained. Numerical examples are given to confirm the theoretical results.

Key words: Nonlinear stability, explicit and diagonally implicit Runge-Kutta methods, neutral functional differential equations, Banach spaces

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显式和对角隐式Rung-Kutta方法求解中立型泛函微分方程的非线性稳定性

NONLINEAR STABILITY OF EXPLICIT AND DIAGONALLY IMPLICIT RUNGE-KUTTA METHODS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

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