首页 | 本学科首页   官方微博 | 高级检索  
     检索      

基于MQ拟插值函数逼近的非线性动力系统数值求解
引用本文:杜珊,李风军.基于MQ拟插值函数逼近的非线性动力系统数值求解[J].应用数学和力学,2017,38(8):943-955.
作者姓名:杜珊  李风军
作者单位:宁夏大学 数学统计学院, 银川 750021
基金项目:61662060)国家自然科学基金(11261024
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.

关 键 词:非线性动力系统    数值方法    MQ拟插值    4阶Runge-Kutta法
收稿时间:2016-11-29

A Numerical Approximation Method for Solutions to Nonlinear Dynamic Systems Based on Multiquadric Quasi-Interpolation Functions
DU Shan,LI Feng-jun.A Numerical Approximation Method for Solutions to Nonlinear Dynamic Systems Based on Multiquadric Quasi-Interpolation Functions[J].Applied Mathematics and Mechanics,2017,38(8):943-955.
Authors:DU Shan  LI Feng-jun
Institution:School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R.China
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.
Keywords:nonlinear dynamic system  numerical method  multiquadric quasi-interpolation  4th-order Runge-Kutta method
本文献已被 CNKI 万方数据 等数据库收录!
点击此处可从《应用数学和力学》浏览原始摘要信息
点击此处可从《应用数学和力学》下载免费的PDF全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号