| 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 |
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| 引用本文： | 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. |
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| 作者姓名： | 苏凯 王锦红 张宏伟 王晚生 |
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| 作者单位： | 1. 长沙理工大学数学与计算科学学院,长沙,410114;湘潭大学数学与计算科学学院,湖南,湘潭,411105
2. 长沙理工大学数学与计算科学学院,长沙,410114 |
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| 基金项目： | 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; 电力青年科技创新资助项目. |
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| 摘 要： | 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．
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| 关 键 词： | 非线性稳定性 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 |
NONLINEAR STABILITY OF EXPLICIT AND DIAGONALLY IMPLICIT RUNGE-KUTTA METHODS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS |
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| 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 on Numerical Methods and Computer Applications,2011,32(1):8-22. |
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| Authors: | Su Kai Wang Jinhong Zhang Hongwei Wang Wansheng |
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| Affiliation: | Su Kai (School of Mathematics and Computational Science,Changsha University of Science and Technology,Changsha 410114,China,School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,China) Wang Jinhong Zhang Hongwei Wang Wansheng (School of Mathematics and Computational Science,China) |
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| Abstract: | 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. |
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| Keywords: | Nonlinear stability explicit and diagonally implicit Runge-Kutta methods neutral functional differential equations Banach spaces |
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