• 论文 •    下一篇

中立型泛函微分方程的多步法

苏德富   

  1. 广西大学
  • 出版日期:1984-03-14 发布日期:1984-03-14

苏德富. 中立型泛函微分方程的多步法[J]. 计算数学, 1984, 6(3): 225-231.

MULTISTEP METHODS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS OF NEUTRAL TYPE

  1. Su De-fu Guangxi University
  • Online:1984-03-14 Published:1984-03-14
在探求泛函微分方程的数值解法时,常常设法把常微分方程的许多古典的有效方法经过改造移殖到泛函微分方程。常微分方程的各种数值方法本质上都是力图使变量离散化。所以,Henrici干脆称之为离散变量法。与常微分方程不同,计算泛函微分方程的解在第n点上的值,不仅与前面某k个点上的值有关,而且往往与这些分点之间的值有关。这是推广过程中遇到的一大困难。1964年Feldstein对时滞微分方程提出了所谓连续Euler法,引进了插值思想,使离散方法连续化,克服了上述困难。1973年Castleton和Crimin把这一方法推广到中立型泛函微分方程。特别是Cryer和Tavernini及
In this paper, the methods of [1] is extended to functional differential equationsof neutral type. We have derived formulas of linear multistep methods for functionaldifferential equations of neutral type by Taylor's method, and developed a iterativealgorithm for implieit methods. Numerical results are provided.
()

[1] L. Tavernini, Linear multistep methods for the numerical solution of volterra functional differential equations, Applicable Analysis, 3: 2(1973) , 169-185.
[2] R. Castleton, L. Crimin, A first order method for differential equations of neutral type, Math.of comp., 27: 123(1973) , 571-577.
[3] M. Feldstein, Discretization Method for Retarded Ordinary Differential Equations, ph. D. Thesis,university of california, Los Angeles, Calf. 1964.
[4] e. w. Cryer, L. Tavernini, The numerical solution of volterra functional differential equations by Euler's method. SIAM J. num. Anal., 9(1972) , 105-129.
[5] L. Tavernini, One-step method for the numerical solution of volterra functional differential equations, SIAM J. num. Anal., 8(1917) , 786-795.
[6] P. Henrici, Discrete variable Method in Ordinary Differential Equations, Wiley, 1962.
No related articles found!
阅读次数
全文


摘要