| 空间中的时滞积分微分方程数值方法及其牛顿迭代解的存在唯一性 |
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| 引用本文： | 张诚坚,吕鹏.空间中的时滞积分微分方程数值方法及其牛顿迭代解的存在唯一性[J].数学物理学报(A辑),2010,30(2):456-464. |
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| 作者姓名： | 张诚坚 吕鹏 |
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| 作者单位： | 华中科技大学数学与统计学院,武汉,430074 |
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| 摘 要： | 该文分析了扩展的一般线性方法关于Banach 空间中一类时滞积分微分方程数值解的可解性, 给出了其方法的解的存在唯一性判据, 并探讨了其Newton迭代解的性态. 所获结果可应用于扩展的Runge-Kutta方法和扩展的线性多步方法等.
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| 关 键 词： | 时滞积分微分方程 解的存在唯一性 数值方法 |
| 收稿时间： | 2008-06-10 |
| 修稿时间： | 2009-08-19 |
Existence and Uniqueness of Numerical Methods and Their Newton-Iterative Solutions for Delay-Integro-Differential Equations on Banach Spaces |
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| ZHANG Cheng-Jian,LU Peng.Existence and Uniqueness of Numerical Methods and Their Newton-Iterative Solutions for Delay-Integro-Differential Equations on Banach Spaces[J].Acta Mathematica Scientia,2010,30(2):456-464. |
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| Authors: | ZHANG Cheng-Jian LU Peng |
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| Institution: | School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074 |
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| Abstract: | This paper analyzes the unique solvability of the extended general linear methods for a class of delay-integro-differential equations on Banach spaces.The criteria for existence and uniqueness of the methods' solutions are derived.Moreover,the properties of Newton iterative solutions are concerned.The obtained results are applicable to the extended Runge-Kutta methods,the extended linear multistep methods and other some methods. |
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| Keywords: | Delay-integro-differential equations Existence and uniqueness of the methods' solutions Numerical methods |
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