基于MQ拟插值函数逼近的非线性动力系统数值求解

杜珊; 李风军

doi:10.21656/1000-0887.370368

基于MQ拟插值函数逼近的非线性动力系统数值求解

doi: 10.21656/1000-0887.370368

杜珊,
李风军

宁夏大学数学统计学院, 银川 750021

基金项目: 国家自然科学基金(11261024；61662060)

详细信息

中图分类号: O29;O302
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- 被引次数: 0
出版历程
- 收稿日期: 2016-11-29
- 修回日期: 2017-01-13
- 刊出日期: 2017-08-15

A Numerical Approximation Method for Solutions to Nonlinear Dynamic Systems Based on Multiquadric Quasi-Interpolation Functions

School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R.China

Funds: The National Natural Science Foundation of China(11261024；61662060)

摘要

摘要: 借助多重二次曲面（multi quadrics，MQ）拟插值函数具有较好精确性和稳定性的优势，研究了基于MQ拟插值函数和4阶Runge-Kutta法相结合的方法，构造了求解带有初值问题的非线性动力系统的数值解法，分析了该方法与已有主要方法的优缺点，并给出了相应的数值算例、误差估计.结果表明该方法计算量小、能很好地逼近非线性动力系统的解析解.
- 非线性动力系统 /
- 数值方法 /
- MQ拟插值 /
- 4阶Runge-Kutta法
Abstract: The multiquadric quasi-interpolation function has advantages of high accuracy and good stability. A new numerical method for resolving the initial value problems of nonlinear dynamic systems was proposed via combination of the multiquadric quasi-interpolation function and the 4th-order Runge-Kutta method. The advantages and disadvantages were analyzed between this new method and the existing numerical methods for nonlinear dynamic systems, according to the numerical example and error estimation. The results show that the proposed method needs less computation cost and enables fine approximation to the analytical solutions to nonlinear dynamic systems.
- nonlinear dynamic system /
- numerical method /
- multiquadric quasi-interpolation /
- 4th-order Runge-Kutta method

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