| 关于求解常微分方程的具有参数的一类预估—校正方法 |
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| 引用本文： | 徐洪义,王长富.关于求解常微分方程的具有参数的一类预估—校正方法[J].南京大学学报(自然科学版),1986(4). |
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| 作者姓名： | 徐洪义 王长富 |
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| 作者单位： | 南京大学数学系，南京大学数学系 |
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| 摘 要： | 本文给出基于由Adams和Nystrom方法的组合、含有参数的一类预估——校正方法,这里预估方法是两个显式方法(A-B和Nystrom)的线性依合,校正方法是两个隐式方法(A-M和M-S)的线性组合。通过对参数的选取,使它们具有增大的绝对稳定区间。对于K=3,4,5,6,7,给出具有扩大绝对稳定区间的预估——校正方法。它们比同阶的Ap_kEC_(k 1)E方法的绝对稳定区间要增大很多。这些方法对求解中等Stiff方程是适合的。
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| 关 键 词： | 预估——校正 绝对稳定区间 Stiff方程组 |
ON THE PREDICTOR-CORRECTOR METHODS WITH PARAMETERS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS |
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| Xu Hongyi Wang Changfu.ON THE PREDICTOR-CORRECTOR METHODS WITH PARAMETERS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS[J].Journal of Nanjing University: Nat Sci Ed,1986(4). |
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| Authors: | Xu Hongyi Wang Changfu |
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| Institution: | Xu Hongyi Wang Changfu |
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| Abstract: | In this paper,a class of predictor-corrector methods with parameters based upon a combination of Adams and Nystrom methods are given. The predictor methods are a linear combination of two explicit formulas(A-B and Nustrom) and the corrector methods are a linear combination of two implicit formulas(A-M and M-S). Within the parameters chosen, methods are obtained that show extended absolute stability intervals. Explicit formulas are given for predictor-corrector methods with the extended absolute stability intervals (for k=3,4,5,6,7)which possess larger stability intervals than that of AP_kEC_(k 1)E with in the same order.Such methods are appropriate for moderately stiff systems. |
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| Keywords: | predictor-corrector absolute stability interval stiff system |
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