| 基于三次样条插值函数的非线性动力系统数值求解 |
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| 引用本文： | 李鹏柱,李风军,李星,周跃亭.基于三次样条插值函数的非线性动力系统数值求解[J].应用数学和力学,2015,36(8):887-896. |
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| 作者姓名： | 李鹏柱 李风军 李星 周跃亭 |
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| 作者单位： | 1宁夏大学 数学计算机学院, 银川 750021;2同济大学 航空航天与力学学院,上海 200092 |
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| 基金项目： | 国家自然科学基金(11261024;11472193;11362108) |
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| 摘 要： | 三次样条插值函数具有良好的收敛性、稳定性与二阶光滑性.研究了借助三次样条插值函数构造的非线性动力系统数值求解方法，分析了该方法与已有的非线性动力系统数值求解方法的优缺点，刻画了误差估计且给出了数值算例.结果表明基于三次样条插值函数构造的数值方法比已有的方法收敛速度快、逼近精度高且能够很好地逼近非线性动力系统的解析解.
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| 关 键 词： | 非线性动力系统 数值方法 三次样条插值 |
| 收稿时间： | 2014-11-25 |
A Numerical Method for the Solutions to Nonlinear Dynamic Systems Based on Cubic Spline Interpolation Functions |
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| Institution: | 1School of Mathematics and Computer Science, Ningxia University, Yinchuan 750021, P.R.China;2School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P.R.China |
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| Abstract: | The cubic spline interpolation function has good convergence, stability and 2nd-order smoothness. A numerical method for the solutions to nonlinear dynamic systems was constructed with the cubic spline interpolation functions. Advantages and disadvantages were compared between this method and the previous numerical methods for nonlinear dynamic systems, with the error estimation conducted in the 2 numerical examples. The results show that the numerical method derived out of the cubic spline interpolation functions has faster convergence rate and higher accuracy than the existing methods, and has good approximation to the analytical solutions to nonlinear dynamic systems. |
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