| 一类特殊的Adams-Moulton公式 |
| |
| 引用本文： | 杨大地,郑兴武.一类特殊的Adams-Moulton公式[J].重庆工学院学报,2007(10). |
| |
| 作者姓名： | 杨大地 郑兴武 |
| |
| 作者单位： | 重庆大学数理学院 重庆400044 |
| |
| 基金项目： | 国家自然科学基金资助项目(10671132) |
| |
| 摘 要： | Adams-Moulton公式是一类k 1阶线性k步法隐式公式,应用十分广泛,但它的绝对稳定区域是有界的,一般不适合用于刚性方程求解.通过改进k步k 1阶Adams-Moulton公式得到了一类更稳定的k阶线性k步法隐式公式:对其中的2步3阶Adams-Moulton公式,改进后可以得到A(α)稳定性;对3步4阶Adams-Moulton公式,改进后可以得到A0稳定性;对4,5步的Adams-Moulton公式,改进后能使有界的绝对稳定区域增大.用数值实验证明了这类公式对解决刚性方程问题的有效性.
|
| 关 键 词： | Adams-Moulton公式 线性多步方法 稳定性 |
Class of Special Adams-Moulton Formulas |
| |
| YANG Da-di,ZHENG Xing-wu.Class of Special Adams-Moulton Formulas[J].Journal of Chongqing Institute of Technology,2007(10). |
| |
| Authors: | YANG Da-di ZHENG Xing-wu |
| |
| Abstract: | The Adams-Moulton formulas are a widely used class of implicit linear k-step formulas of(k 1)-order.But their regions of absolute stability are bounded and can't be used to solve stiff equations generally.One class of a more stable implicit linear k-step formulas of k-order can be obtained by improving k-step Adams-Moulton formulas of k 1-order.By improving 2-step Adams-Moulton formula of order 3,stability of 3-step formula of order 3 can be reached;by improving 3-step Adams-Moulton formula of order 4,stability of 4-step formulas of order 4 can be obtained;and by improving 4,5-step Adams-Moutlon formulas,the regions of the formulas of absolute stability are enlarged.Besides,the validity for stiff equations is verified by numerical experiments. |
| |
| Keywords: | Adams-Moulton formula linear multi-step method stability |
| 本文献已被 CNKI 等数据库收录！ |
|
