一类A(α)稳定的k阶线性k步法公式  

A NEW CLASS OF A(α)-STABLE k-STEP IMPLICIT METHODS OF ORDER k

作　　者：杨大地[1] 刘冬兵[2] 

机构地区：[1]重庆大学数理学院,重庆400044 [2]攀枝花学院计算机学院,四川攀枝花617000

出　　处：《计算数学》2008年第2期143-146,共4页Mathematica Numerica Sinica

基　　金：国家自然科学基金项目(10671132)资助．

摘　　要：本文给出了一类与Gear方法类似的k阶线性k步法隐式公式.作者还求出了公式的分数形式的系数,阶数和局部截断误差主项系数,并验证了2-6步公式都具有A(α)稳定的,计算出了它们的幅角α.最后用对比数值实验验证了公式确实是稳定的,并且适合于求解刚性常微分方程.In this paper a new class of linear k-step implicit methods of order k,similar to Gear methods, is given. The fractal coefficients of the formulas of order 2 to 6 in this class are deduced,the orders and error coefficients are also gotten. Then we proved that they are A（α）- stable and the radiant angles of stability α are 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：线性多步方法 A(α)稳定性 刚性常微分方程 数值实验 

分 类 号：O241.81[理学—计算数学]