Volterra泛函微分方程的(A,B,D)方法  

(A,B,D)-METHODS FOR VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATIONS

作　　者：李寿佛[1] 易梦红 

机构地区：[1]湘潭大学数学系

出　　处：《高等学校计算数学学报》1991年第3期221-236,共16页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金

摘　　要：1 引言 1966年,Butcher提出并研究了一类十分广泛的常微分方程数值方法——(A,B)方法本文目的是试图将(A,B)方法适当修改,使之成为适于求解Volterra泛函微分方程的数值方法,我们称如此得到的新方法为(A,B,D)-方法,(A,B,D)-方法的概括面非常广泛。In this paper, general multivalue methods for Volterra functional differential equations, which are called (A,B,D)-methods, are constructed. A series of sufficient and necessary conditions for stability, consistency and convergence of these methods is obtained. Since these methods include almost every method which is commonly used to solve Volterra functional differential equations, the theory developed in this paper is therefore of general significance. The mumerical experiments at the end of this paper confirm our theoretical analysis and show the practical meaning of these methods.

关 键 词：泛函微分方程 数值解法 VOLTERRA 

分 类 号：O241.8[理学—计算数学]