%0 Journal Article
%T 小波法求解分数阶微分方程组及其收敛性分析<br>Wavelets method for solving system of fractional differential equations and the convergence analysis
%A 陈一鸣
%A 柯小红
%A 韩小宁
%A 孙艳楠
%A 刘立卿&lt
%A br&gt
%A CHEN Yi-ming
%A KE Xiao-hong
%A HAN Xiao-ning
%A SUN Yan-nan
%A LIU Li-qing
%J 山东大学学报（理学版）
%D 2015
%R 10.6040/j.issn.1671-9352.0.2014.078
%X 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.<br>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
%K 分数阶微分方程组
%K 收敛性分析
%K 算子矩阵
%K 移位的Legendre多项式
%K Legendre小波
%K &lt
%K br&gt
%K Legendre wavelets
%K operational matrix
%K convergence analysis
%K system of fractional differential equations
%K shifted Legendre polynomial
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2014.078