数学物理学报 ›› 2010, Vol. 30 ›› Issue (2): 456-464.

• 论文 • 上一篇    下一篇

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

张诚坚, 吕鹏   

  1. 华中科技大学 数学与统计学院, 武汉 430074
  • 收稿日期:2008-06-10 修回日期:2009-08-19 出版日期:2010-04-25 发布日期:2010-04-25
  • 基金资助:

    国家自然科学基金(10871078)资助.

Existence and Uniqueness of Numerical Methods and Their Newton-Iterative Solutions for Delay-Integro-Differential Equations on Banach Spaces

 ZHANG Cheng-Jian, LU Peng   

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074
  • Received:2008-06-10 Revised:2009-08-19 Online:2010-04-25 Published:2010-04-25
  • Supported by:

    国家自然科学基金(10871078)资助.

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.

关键词: 时滞积分微分方程, 解的存在唯一性, 数值方法

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.

Key words: Delay-integro-differential equations, Existence and uniqueness of the methods solutions, Numerical methods

中图分类号: 

  • 65L20