Legendre多项式求解变系数的分数阶Fredholm积分微分方程

J4 ›› 2013, Vol. 48 ›› Issue (6): 80-86.

Legendre多项式求解变系数的分数阶Fredholm积分微分方程

陈一鸣,孙慧,刘乐春，付小红

燕山大学理学院, 河北秦皇岛 066004

收稿日期:2012-11-15 出版日期:2013-06-20 发布日期:2013-06-09
作者简介:陈一鸣（1957- ），男，博士，教授，研究方向为分数阶微分方程.Email:chenym@ysu.edu.cn
基金资助:
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)

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

HEN Yi-ming, SUN Hui, LIU Le-chun, FU Xiao-hong

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

Received:2012-11-15 Online:2013-06-20 Published:2013-06-09

摘要/Abstract

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。

关键词: Legendre多项式; 分数阶微分; 变系数; Caputo导数; 数值解

Abstract:

In order to solve the Fredholm integro-differential equations of fractional order with variable coefficient, By using 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 numerical solution are obtained. A numerical example is presented, which verifying the feasibility and effectiveness of the method.

Key words: Legendre polynomial; fractional calculus; variable coefficient; Caputo derivative; numerical solution

陈一鸣,孙慧,刘乐春，付小红. Legendre多项式求解变系数的分数阶Fredholm积分微分方程[J]. J4, 2013, 48(6): 80-86.

HEN Yi-ming, SUN Hui, LIU Le-chun, FU Xiao-hong. Legendre polynomial method for solving Fredholm integro-differential equations of fractional order with variable coefficient[J]. J4, 2013, 48(6): 80-86.

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