| 基于拟Legendre多项式求解一类分数阶微分方程 |
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| 引用本文： | 陈一鸣,孙艳楠,刘立卿,柯小红.基于拟Legendre多项式求解一类分数阶微分方程[J].计算数学,2015,37(1):21-33. |
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| 作者姓名： | 陈一鸣 孙艳楠 刘立卿 柯小红 |
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| 作者单位： | 燕山大学理学院, 河北秦皇岛 066004 |
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| 基金项目： | 河北省自然科学基金(A2012203047)资助项目;秦皇岛市科学技术研究与发展计划(201201B019)资助项目;秦皇岛市科技局2013科学技术研究与发展计划(201302A023). |
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| 摘 要： | 本文基于移位的Legendre多项式构造一类新的正交拟Legendre多项式求解一类分数阶微分方程.用阶数随所求未知函数的微分的阶数而变化的拟Legendre多项式逼近未知函数;利用分数阶积分的性质推导拟Legendre多项式的积分算子阵,结合算子矩阵的思想和Tau方法,将问题转化为求解代数方程组的问题.最后,给出数值算例证明该方法的有效性.
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| 关 键 词： | 拟Legendre多项式 分数阶微分方程 数值解 算子矩阵 |
| 收稿时间： | 2014-01-08; |
BASED ON FRACTIONAL-ORDER LEGENDRE FUNCTIONS SOLVING A CLASS OF FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS |
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| Chen Yiming,Sun Yannan,Liu Liqing,Ke Xiaohong.BASED ON FRACTIONAL-ORDER LEGENDRE FUNCTIONS SOLVING A CLASS OF FRACTIONAL-ORDER DIFFERENTIAL EQUATIONS[J].Mathematica Numerica Sinica,2015,37(1):21-33. |
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| Authors: | Chen Yiming Sun Yannan Liu Liqing Ke Xiaohong |
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| Institution: | College of Sciences, Yanshan University, Qinhuangdao 066004, Hebei, China |
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| Abstract: | In this article, a general formulation for the fractional-order Legendre functions(FLFS) is constructed to obtain the solution of fractional-order differential equations. Fractional-order Legendre Functions whose order is the same to the order of the fractional differential is used to approximation the unknown function. Also a general formulation for FLFS fractional integral operational matrix is driven. These matrices together with the Tau method are then utilized to reduce the solution of this problem to the solution of a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. |
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| Keywords: | Fractional-order Legendre functions Fractional differential equations Operational matrix Numerical solution |
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