具有A(α)-稳定的Adams-Moulton公式类型  

A(α)-Stability of Adams-Moulton Type Methods

作　　者：刘冬兵 林宗兵 谭千蓉 LIU Dong-bing;LIN Zong-bing;TAN Qian-rong(College of Mathematics and Computer,Panzhihua University,Panzhihua 617000,China)

机构地区：[1]攀枝花学院数学与计算机学院,四川攀枝花617000

出　　处：《数学的实践与认识》2020年第17期187-193,共7页Mathematics in Practice and Theory

基　　金：四川省科技厅应用基础研究项目(2019YJ0683);攀枝花市市级科研项目(2019ZD-R-1);攀枝花学院校级科研项目(2016ZD010)。

摘　　要：给出了含参数的3阶3步法的A(α)-稳定的Adams-Moulton类型公式族.同时求出了公式的精确分数形式的系数,阶数和局部截断误差主项系数,计算出了它们的幅角α,最后用对比数值实验验证了公式是稳定的,并且适合于求解刚性常微分方程.In this paper Adams-Moulton type method of step three and oerdr three with stable parameter is given.The fractal coefficients of the formulas are deduced,the orders and error coefficients are also gotten.Then we proved that they are A(α)-stable and the radiant angles of stabilityαare given.Finally,by means of the comparison numerical experiment,it is verified that they are stable and suitable for solving initial value problems of stiff ordinary differential equations.

关 键 词：Adams-Moulton方法 A(α)-稳定性 刚性常微分方程 数值实验 

分 类 号：O175.1[理学—数学]