| 常微分方程差分周期解的几何性质 |
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| 引用本文： | 张丽清 刘颖. 常微分方程差分周期解的几何性质[J]. 华南理工大学学报(自然科学版), 1992, 20(2): 16-22 |
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| 作者姓名： | 张丽清 刘颖 |
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| 作者单位： | 华南理工大学自动化系，华南理工大学自动化系 |
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| 摘 要： | 本文讨论常微分方程差分周期解的几何性质。首先讨论了隐差分解与显差分解的关系,并利用差分解的渐近展开式构造差分校正解来提高精度。然后证明了差分周期解的凸性不变性。最后提出周期解单侧逼近的判别方法,得出了差分周期解单侧逼近的条件。
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| 关 键 词： | 差分法 周期解 常微分方程 |
GEOMETRIC PROPERTIES OF DIFFERENCE PERIODIC SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS |
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| Zhang Liqing Liu Ying. GEOMETRIC PROPERTIES OF DIFFERENCE PERIODIC SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS[J]. Journal of South China University of Technology(Natural Science Edition), 1992, 20(2): 16-22 |
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| Authors: | Zhang Liqing Liu Ying |
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| Abstract: | In this paper the geometric properties of the difference periodic solutions of ordinary differential equations are discussed. The relation between the explicit difference solution and the implicit one is established.A correction difference solution with higher accuracy is constructed by the use of asymptotic expansion.Then it is proved that the difference periodic orbit preserves the convexity of periodic orbit.Finally a new technique is developed to study one-side approximation of numerical solutions and the condition of inner(or outer)approximation is also given. |
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| Keywords: | differencemethods periodic solutions asymptotic expansions/geometric properties one-side approximation |
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