| 一类A(α)稳定的k阶线性k步法公式 |
| |
| 引用本文： | 杨大地,刘冬兵.一类A(α)稳定的k阶线性k步法公式[J].计算数学,2008,30(2):143-146. |
| |
| 作者姓名： | 杨大地 刘冬兵 |
| |
| 作者单位： | 杨大地（重庆大学数理学院,重庆,400044）;刘冬兵（攀枝花学院计算机学院,四川,攀枝花,617000） |
| |
| 摘 要： | 本文给出了一类与Gear方法类似的κ阶线性κ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.
|
| 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 |
| 修稿时间： | 2006年10月15 |
A NEW CLASS OF A(α)-STABLE k-STEP IMPLICIT METHODS OF ORDER k |
| |
| Yang Dadi,Liu Dongbing.A NEW CLASS OF A(α)-STABLE k-STEP IMPLICIT METHODS OF ORDER k[J].Mathematica Numerica Sinica,2008,30(2):143-146. |
| |
| Authors: | Yang Dadi Liu Dongbing |
| |
| Institution: | Yang Dadi (College of Mathematics and Physics,ChongQing University,Chongqing 400044,China) Liu Dongbing (Department of Computer,Panzhihua University,Panzhihua 617000,Sichuan,China) |
| |
| Abstract: | 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 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. |
| |
| Keywords: | |
| 本文献已被 万方数据 等数据库收录！ |
| 点击此处可从《计算数学》浏览原始摘要信息 |
| 点击此处可从《计算数学》下载免费的PDF全文 |
|
