拓展的Adams-Moulton方法(英文)

本文以 k 步 Adams-Moulton(A—M)公式作为“预估式”,以带有拓展项 hβ_(k+1)f_(n+k+l)的 A—M 型公式作为校正式,形成一种具有隐式预估式的预估——校正法,即所谓拓展的A—M 方法。和 k 步 A—M 法相比,拓展的 A—M 法有较高的精度阶(p=k+2)和较大的稳定性区域,特别当 k=2时,方法是几乎 A 定稳的。计算量虽然大一些,但可设法节省许多。     

确定微分一代数方程系统指数的一个过程

一般非线性微分——代数方程系统可以写成F(y′,y,t)=0(1)其中 F、y′、y 都是维数相同的向量,在某种意义上,最简单的是线性、常系数微分——代数方程系统Ay′+By=g(t),(2)这系统可通过矩阵束(A,B)的 Kronecker 标准形得到完全了解.Gantmacher〔1〕对一     

EXISTENDED SECOND DERIVATIVE METHODS FOR SOLVING STIFF SYSTEMS OF ODEs

In this paper a class of the extended second derivative formulas is presented. Based on the extended k-step second derivative formula a new predictor-corrector method called Extended k-step second Derivative Method for stiff systems is formulated with the k-step second derivative formula as its implicit predictor. The extended second derivative methods have the higher orders and the better stability properties. The computational effort is comparitively large, but much of it can be saved, so that the methods are acceptable and efficient.