中立型延迟积分微分方程线性θ-方法的渐近稳定性

J4 ›› 2010, Vol. 45 ›› Issue (1): 102-106.

中立型延迟积分微分方程线性θ-方法的渐近稳定性

余越昕刘忠艳江春华

湘潭大学数学系, 湖南湘潭 411105

收稿日期:2009-04-07 出版日期:2010-01-16 发布日期:2010-03-25
作者简介:余越昕(1968-), 男, 副教授, 博士, 研究方向为泛函微分方程算法理论及应用.Email: yuyx@xtu.edu.cn
基金资助:
国家自然科学基金资助项目(10871164)；湖南省教育厅优秀青年项目(07B072)；湖南省自然科学基金资助项目(08JJ6002)

Asymptotic stability of linear θ-methods for neutral delay integro-differential equations

Department of Mathematics, Xiangtan University, Xiangtan 411105, Hunan, China

Received:2009-04-07 Online:2010-01-16 Published:2010-03-25

摘要/Abstract

摘要：

将线性θ-方法用于求解D(α,β₁,β₂,β3,γ,δ)类非线性中立型延迟积分微分方程,结果表明A-稳定的线性θ-方法(也即1／2≤θ≤1)能保持问题本身的渐近稳定性,数值实验验证了所获理论结果的正确性。

关键词: 中立型延迟积分微分方程; 线性θ-方法; 渐近稳定性

Abstract:

Linear θ-methods are adapted for solving a class D(α,β₁,β₂,β3,γ,δ) of nonlinear neutral delay integro-differential equations (NDIDEs). It is proved that an A-stable linear θ-method (i.e. 1／2≤θ≤1) can preserve the asymptotic stability of the underlying systems of NDIDEs. A numerical test isgiven, which confirms the theoretical results in the end.

Key words: neutral delay integro-differential equations; linearθ-methods; asymptotic stability

余越昕刘忠艳江春华. 中立型延迟积分微分方程线性θ-方法的渐近稳定性[J]. J4, 2010, 45(1): 102-106.

YU Yue-Xin, LIU Zhong-Yan, JIANG Chun-Hua. Asymptotic stability of linear θ-methods for neutral delay integro-differential equations[J]. J4, 2010, 45(1): 102-106.

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