| 一类隐式的k+1阶线性k步法 |
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| 引用本文： | 刘冬兵,马亮亮.一类隐式的k+1阶线性k步法[J].计算数学,2013,35(4):393-400. |
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| 作者姓名： | 刘冬兵 马亮亮 |
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| 作者单位： | 攀枝花学院数学与计算机学院, 四川攀枝花 617000 |
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| 基金项目： | 国家自然科学基金（10671132）资助项目，四川省科技厅自然科学基金项目（2013JY0125）和攀枝花学院自然科学基金项目（2012YB21）资助。 |
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| 摘 要： | 本文首先给出了一类比Adams-Moulton方法的绝对稳定区间大的隐式k+1阶线性k步法基本公式.求出了3-9步新公式的分数形式的精确系数，阶数，局部截断误差主项系数和绝对稳定区间，然后构造了由4阶隐式新公式和同阶显式Nyström公式组合而成的预估-校正方法，比著名的Adams-Bashforth-Moulton和Nyström-Adams-Moulton预估校正方法的绝对稳定区间大，最后用对比数值试验对结果进行了验证.
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| 关 键 词： | 线性多步法 稳定性 预估—校正方法 数值试验 |
| 收稿时间： | 2013-03-15; |
A CLASS OF k STEP LINEAR MULTISTEP IMPLICIT METHODS OF k+1 ORDER |
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| Liu Dongbing,Ma Liangliang.A CLASS OF k STEP LINEAR MULTISTEP IMPLICIT METHODS OF k+1 ORDER[J].Mathematica Numerica Sinica,2013,35(4):393-400. |
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| Authors: | Liu Dongbing Ma Liangliang |
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| Institution: | College of Mathematics and Computer, Panzhihua University, Panzhihua 617000, Sichuan, China |
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| Abstract: | In this paper, a new class basic formulas of linear k step implicit methods of k+1 order, the stability better than Adams-Moulton methods, is given. The fractal coefficients of the formulas of 3-step to 9 in this class are deduced, the orders and error coefficients are also gotten. We computed their absolute stability interval. It is that the absolute stability interval of predictor-corrector method composed of a new 4 order explicit formula and a new 4 order implicit basic formula large than well-known Adams-Bashforth-Moulton and Nyström-Adams-Moulton predictor-corrector method.Finally, by means of the numerical experiment, it is verified that are stable. |
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| Keywords: | Linear multistep methods Stability Predictor-corrector methods Numerical experiment |
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