小波法求解分数阶微分方程组及其收敛性分析

doi:10.6040/j.issn.1671-9352.0.2014.078

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (02): 67-74.doi: 10.6040/j.issn.1671-9352.0.2014.078

小波法求解分数阶微分方程组及其收敛性分析

陈一鸣, 柯小红, 韩小宁, 孙艳楠, 刘立卿

燕山大学理学院, 河北秦皇岛 066004

收稿日期:2014-03-05 修回日期:2014-11-03 出版日期:2015-02-20 发布日期:2015-01-27
通讯作者: 柯小红(1989-),女,硕士,研究方向为分数阶微积分. E-mail:kexiaohong1989@163.com E-mail:kexiaohong1989@163.com
作者简介:陈一鸣(1957-),男,博士,教授,研究方向为分数阶微积分. E-mail:chenym@ysu.edu.cn
基金资助:
河北省自然科学基金资助项目(A2012203047)

Wavelets method for solving system of fractional differential equations and the convergence analysis

CHEN Yi-ming, KE Xiao-hong, HAN Xiao-ning, SUN Yan-nan, LIU Li-qing

College of Science, Yanshan University, Qinhuangdao 066004, Hebei, China

Received:2014-03-05 Revised:2014-11-03 Online:2015-02-20 Published:2015-01-27

摘要/Abstract

摘要： 应用Legendre小波求解一类变系数分数阶微分方程组,利用Legendre小波积分算子矩阵将微分方程组转化成易于求解的代数方程组形式,进而对其进行求解.给出Legendre小波近似未知函数的收敛性分析,证明该方法的正确性,并给出三个数值算例进一步说明该方法是可行并有效的.

关键词: 分数阶微分方程组, 收敛性分析, 算子矩阵, 移位的Legendre多项式, Legendre小波

Abstract: The Legendre wavelets defined by the shifted Legendre polynomial is used to solve the numerical solution of the system of fractional differential equations with variable coefficient.The convergence analysis is presented to show that this method is correct for solving the fractional differential equations. Finally, three numerical examples are given to demonstrate the feasibility and efficiency of this method.

Key words: Legendre wavelets, operational matrix, convergence analysis, system of fractional differential equations, shifted Legendre polynomial

中图分类号:

O241.8

陈一鸣, 柯小红, 韩小宁, 孙艳楠, 刘立卿. 小波法求解分数阶微分方程组及其收敛性分析[J]. 山东大学学报（理学版）, 2015, 50(02): 67-74.

CHEN Yi-ming, KE Xiao-hong, HAN Xiao-ning, SUN Yan-nan, LIU Li-qing. Wavelets method for solving system of fractional differential equations and the convergence analysis[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 67-74.

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小波法求解分数阶微分方程组及其收敛性分析

Wavelets method for solving system of fractional differential equations and the convergence analysis

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