应用Haar小波求解非线性分数阶Fredholm积分微分方程  

Haar Wavelet Method for Solving Nonlinear Fredholm Integro-differential Equations of Fractional Order

作　　者：仪明旭[1] 陈一鸣[1] 魏金侠[1] 刘玉风[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《河北师范大学学报（自然科学版）》2012年第5期452-455,共4页Journal of Hebei Normal University：Natural Science

基　　金：河北省自然科学基金(E2009000365)

摘　　要：Fredholm积分微分方程的数值算法一直是近些年来研究的重要课题.利用Haar小波研究了非线性分数阶Fredholm积分微分方程.Haar小波具有正交性,可计算性以及小支集性.结合block pulse函数给出了Haar小波的分数阶积分算子矩阵,并利用该函数的定义与Haar小波的积分算子矩阵的性质,将非线性分数阶Fredholm积分微分方程转换为非线性代数方程,从而便于计算机求解.最后给出算例表明该方法的有效性.In recent years,the numerical algorithm of Fredholm integro-differential equations is always the important topic.The numerical solution of nonlinear Fredholm integro-differential equations of fractional order is discussed by using Haar wavelet.Haar wavelet is orthogonal,computational,and has a small support.The integral operational matrix of fractional order of Haar wavelet through the block pulse functions is given.Making use of the definition of block pulse functions and the properties of integral operational matrix of fractional order of Haar wavelet,reduces the problem to a nonlinear system of algebraic equations,and then it becomes convenient for computers to calculus.Finally,the numerical example shows that the method is effective.

关 键 词：HAAR小波 Fredholm积分微分方程 非线性 算子矩阵 BLOCK pulse函数 数值解 

分 类 号：O241.8[理学—计算数学]