上海大学学报(自然科学版) ›› 2020, Vol. 26 ›› Issue (3): 456-471.doi: 10.12066/j.issn.1007-2861.2052

• 研究论文 • 上一篇    下一篇

非线性泛函积分微分方程的多步龙格-库塔方法的耗散性

张艳()   

  1. 上海大学 理学院, 上海 200444
  • 收稿日期:2018-03-26 出版日期:2020-06-30 发布日期:2020-01-31
  • 通讯作者: 张艳 E-mail:1653287436@qq.com

Dissipativity of multistep Runge-Kutta methods for a class of nonlinear functional-integro-differential equations

ZHANG Yan()   

  1. College of Sciences, Shanghai University, Shanghai 200444, China
  • Received:2018-03-26 Online:2020-06-30 Published:2020-01-31
  • Contact: ZHANG Yan E-mail:1653287436@qq.com

摘要:

研究了非线性泛函积分微分方程系统数值解的耗散性, 给出了关于这类方程的多步龙格-库塔方法的耗散性的充分条件, 进一步利用数值算例验证了该方法的主要结果.

关键词: 泛函积分微分方程, 多步龙格-库塔方法, 耗散性, 代数稳定性, 动力系统

Abstract:

In this paper, the dissipation of numerical solutions for nonlinear functional-integro-differential equations is studied. A sufficient condition of the dissipation of the multistep Runge-Kutta method is presented for the equation. Furthermore, a numerical example is given to illustrate the main result of this paper.

Key words: functional-integro-differential equation, Multistep R-K methods, Dissipativity, Algebraic stability, Dynamical systems

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