一类求解分片延迟微分方程的线性多步法的散逸性  

DISSIPATIVITY OF LINEAR MULTISTEP METHODS FOR NONLINEAR DIFFERENTIAL EQUATIONS WITH PIECEWISE DELAYS

作　　者：文立平[1] 余越昕[1] 李寿佛[1] 

机构地区：[1]湘潭大学数学与计算科学学院,湘潭411105

出　　处：《计算数学》2006年第1期67-74,共8页Mathematica Numerica Sinica

基　　金：国家自然科学基金资助项目(No.10271100;NO.10571147);湖南省教育厅重点科研项目(04A057)资助

摘　　要：本文研究分片延迟微分方程本身及数值方法的散逸性问题．给出了一个关于此类问题本身散逸性的充分条件,同时得到了一类求解此类问题的线性多步法的数值散逸性结果,此结果表明所考虑的数值方法继承了方程本身的散逸性．数值试验进一步验证了理论结果的正确性．This paper is concerned with the dissipativity of theoretical solution and numerical solution of a class of nonlinear differential equations with piecewise delays. At first, a sufficient condition for the dissipativity of theoretical solution of the mentioned problem above is given, then the dissipativity results are obtained for a class of linear multistep methods when they are applied to these problems and the gained result shows that the numerical methods inherit the dissipativity of the underlying problem. Several numerical tests are given that confirm the theoretical results.

关 键 词：动力系统 分片延迟 散逸性 线性多步法 

分 类 号：O241.8[理学—计算数学] O241.81[理学—数学]