| 贺群,徐伟.迭代图胞映射方法的快速生成实现[J].计算力学学报,2011,28(5):803~806 |
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| 迭代图胞映射方法的快速生成实现 |
| Fast implementing of the iterative digraph cell mapping |
| 投稿时间：2010-05-20 修订日期：2010-10-26 |
| DOI：10.7511/jslx201105026 |
| 中文关键词: 迭代图胞映射方法 符号计算 龙格库塔法 杜芬方程 非线性 |
| 英文关键词:Iterative digraph cell mapping method Symbol computation Runge-Kutta schemes Duffing equation Nonlinear |
| 基金项目:国家自然科学基金(10872165,10802061)资助项目. |
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| 中文摘要: |
| 在迭代图胞映射方法的框架下,基于摄动微分多项式的思想讨论了常微分方程的快速求解,将所得结果与迭代图胞映射方法有机结合,有效地解决了迭代图胞映射动力系统的快速生成问题,克服了微分方程动力系统生成迭代图胞映射系统过程中耗时较多、效率低下的不足,大大提高了计算效率。通过对典型非线性系统——杜芬方程的应用分析,证实了该方法的有效性。 |
| 英文摘要: |
| Cell mapping is an effective method of global analysis of dynamical systems. In order to overcome the drawback of low efficiency of generating the cell mapping dynamical system from the dynamical system described by the differential equation, this paper improves the Expanded Point Mapping method based on the iterative digraph cell mapping method. Through the combination of the fast calculating of the ordinary differential equation and the iterative digraph cell mapping method, it shows that the presented technique can solve the problem of fast generating of the cell mapping dynamical system, and remarkably improve the calculating efficiency. As an illustrative example, the duffing equation is taken to demonstrate the validity and efficiency of this method. |
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