Legendre多项式求解变系数的分数阶Fredholm积分微分方程  

Legendre polynomial method for solving Fredholm integro-differential equations of fractional order with variable coefficient

作　　者：陈一鸣[1] 孙慧[1] 刘乐春[1] 付小红[1] 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《山东大学学报（理学版）》2013年第6期80-86,共7页Journal of Shandong University(Natural Science)

基　　金：河北省自然科学基金资助项目(A2012203047);秦皇岛市重大科学技术项目(201201B019)

摘　　要：为了求解变系数分数阶Fredholm微积分方程的数值解,运用Caputo分数阶导数及性质,得出了由Legendre多项式构造的任意分数阶微分算子Dα,再利用区间[0,1]上Legendre级数的逼近,将变系数的分数阶微积分方程用矩阵形式表示,采用配点法,得到相应的代数方程组,对原微积分方程的数值解进行了研究并给出了数值算例,验证了Legendre多项式方法的可行性和有效性。In order to solve the Fredholm integro-differential equations of fractional order with variable coefficient, By u- sing Caputo fractional derivative and property, the arbitrary order derivatives expressed by Legendre polynomial are acquired, then using Legendre series on the approximation in the interval, the fractional integral differential equations can be changed into matrix form of the equation, using collocation method. The original integral differential equations nu- merical solution are obtained. A numerical example is presented, which verifying the feasibility and effectiveness of the method.

关 键 词：LEGENDRE多项式 分数阶微分 变系数 CAPUTO导数 数值解 

分 类 号：O241.8[理学—计算数学]