| 一般线性方法的线性与非线性稳定性间的关系 |
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| 引用本文： | 阮保庚.一般线性方法的线性与非线性稳定性间的关系[J].计算数学,2000,22(1):13-20. |
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| 作者姓名： | 阮保庚 |
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| 作者单位： | 番禺师专数学系,番禺,511400 |
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| 摘 要： | １．引言１９６３年，Ｄａｈｌｑｕｉｓｔ以一类线性问题为模型提出了Ａ－稳定性概念，此后有关如何判断方法是否Ａ－稳定或确定其稳定域的研究十分活跃，袁兆鼎等~［１］中对此有详细的讨论．Ｂｕｒｒａｇｅ与Ｂｕｔｃｈｅｒ［２］以一类非线性问题为模型，就一般线性方法引入了代数稳定性概念．Ｂｕｔｃｈｅｒ［４］探讨了代数稳定性与Ａ－稳定性间的内在联系．为确保代数稳定性蕴涵Ａ－稳定性，Ｂｕｔｃｈｅｒ［５］进一步要求代数稳定性定义中涉及的矩阵Ｇ是正定的。然而这样一来，正如李寿佛［６］中指出的那样，许多ＡＮ稳定且按［４…
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| 关 键 词： | 数值分析 一般线性方法 稳定性 线性 非线性 |
THE RELATION BETWEEN LINEAR AND NONLINEAR STABILITY OF GENERAL LINEAR METHODS |
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| Ruan Baogen.THE RELATION BETWEEN LINEAR AND NONLINEAR STABILITY OF GENERAL LINEAR METHODS[J].Mathematica Numerica Sinica,2000,22(1):13-20. |
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| Authors: | Ruan Baogen |
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| Institution: | Ruan Baogen (Panyu Teacher's College, Panyu, 511400) |
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| Abstract: | Some new concepts of stability are introduced for general linear methods, and algebraic conditions for stability of the methods are proposed which are suitable not only for implicit methods but also for explicit methods. Our results characterize the interrelation between linear and nonlinear stability so that new evidence for the construction of efficient and stable methods is offered. |
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| Keywords: | Numerical analysis general linear methods stability |
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