• 论文 •

### 非线性延迟积分微分方程连续Runge-Kutta方法的稳定性分析

1. 广西师范大学数学与统计学院, 桂林 541004
• 收稿日期:2015-10-08 出版日期:2017-02-15 发布日期:2017-02-17
• 通讯作者: 肖飞雁, E-mail:fyxiao@mailbox.gxnu.edu.cn.
• 基金资助:

国家自然科学基金资助项目（Nos.11301099，11461008），广西高等学校高水平创新团队及卓越学者计划资助.

Xiao Feiyan, Li Xuxu, Chen Feisheng. STABILITY ANALYSIS OF CONTINUOUS RUNGE-KUTTA METHODS FOR NONLINEAR DELAY INTEGRO-DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2017, 39(1): 1-13.

### STABILITY ANALYSIS OF CONTINUOUS RUNGE-KUTTA METHODS FOR NONLINEAR DELAY INTEGRO-DIFFERENTIAL EQUATIONS

Xiao Feiyan, Li Xuxu, Chen Feisheng

1. School of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China
• Received:2015-10-08 Online:2017-02-15 Published:2017-02-17

In this paper,continuous Runge-Kutta methods are applied to solve general nonlinear delay integro-differential equations,and a class of numerical algorithms is suggested.The stability of the numerical algorithms is studied,and it is proved that the numerical algorithms are asymptotically stable when the Runge-Kutta methods are (k,l)-algebraically stable and 0 < k < 1.Numerical experiments are used to validate the theoretical results and the effectiveness of the numerical algorithms.

MR(2010)主题分类:

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