[1]牛红玲,郝玲,余志先.算子矩阵法求高阶弱奇异积分微分方程数值解[J].华侨大学学报(自然科学版),2013,34(5):581-585.[doi:10.11830/ISSN.1000-5013.2013.05.0581]
 NIU Hong-ling,HAO ling,YU Zhi-xian.Operational Matrix Method for Solving the Numerical Solution of High Order Integro-Differential Equation with Weakly Singular[J].Journal of Huaqiao University(Natural Science),2013,34(5):581-585.[doi:10.11830/ISSN.1000-5013.2013.05.0581]
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算子矩阵法求高阶弱奇异积分微分方程数值解()
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《华侨大学学报(自然科学版)》[ISSN:1000-5013/CN:35-1079/N]

卷:
第34卷
期数:
2013年第5期
页码:
581-585
栏目:
出版日期:
2013-09-20

文章信息/Info

Title:
Operational Matrix Method for Solving the Numerical Solution of High Order Integro-Differential Equation with Weakly Singular
文章编号:
1000-5013(2013)05-0581-05
作者:
牛红玲1 郝玲1 余志先2
1. 河北民族师范学院 数学与计算机系, 河北 承德 067000;2. 上海理工大学 理学院, 上海 200093
Author(s):
NIU Hong-ling1 HAO ling1 YU Zhi-xian2
1. Department of Mathematics and Computer Science, Hebei Teachers College for Nationalities, Chengde 067000, China; 2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
关键词:
高阶变系数 弱奇异积分 积分微分方程 Legendre多项式 算子矩阵 数值解
Keywords:
high order variable coefficients weakly singular integral integro-differential equation Legendre polynomial operational matrix numerical solution
分类号:
O241.8
DOI:
10.11830/ISSN.1000-5013.2013.05.0581
文献标志码:
A
摘要:
利用Legendre多项式的定义和性质,给出Legendre多项式微分算子矩阵,得到任意阶弱奇异积分的近似求积公式,并将原方程转换为代数方程.收敛性分析说明该方法是收敛的,数值算例验证了该方法的有效性和理论分析的正确性.
Abstract:
One derivative operational matrix of Legendre polynomials is given by using the definition of Legendre polynomials and some properties. And an approximate formula which solves solution of arbitrary order weakly singular integral is also obtained and the original equation is transformed into algebraic equation. Convergence analysis shows that the method is convergent. Finally, numerical example is provided to verify the validity of the method and the correctness of the theoretical analysis.

参考文献/References:

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[8] HOSSEINI S M,SHAHMORAD S.Numerical solution of a class of Integro-differential equations by the tau method with an error estimation[J].Appl Math Comput,2003,136(2/3):559-570.
[9] SAADATMANDI A,DEHGHAN M.A new operational matrix for solving fractional-order differential equations[J].Computers and Mathematics with Applications,2010,59(3):1326-1336.
[10] YALCINBAS S,SEZER M,SOUKUN H H.Legendre polynomial solutions of high-order linear Fredholm integro-differential equations[J].Appl Math Comput,2009,210(2):334-349.

相似文献/References:

[1]单锐,魏金侠,张雁.Bernstein算子矩阵法求高阶弱奇异积分微分方程数值解[J].华侨大学学报(自然科学版),2012,33(5):595.[doi:10.11830/ISSN.1000-5013.2012.05.0595]
 SHAN Rui,WEI Jinxia,ZHANG Yan.Bernstein Operational Matrix Method for Solving the Numerical Solution of High Order Integro-Differential Equation with Weakly Singular[J].Journal of Huaqiao University(Natural Science),2012,33(5):595.[doi:10.11830/ISSN.1000-5013.2012.05.0595]

备注/Memo

备注/Memo:
收稿日期: 2013-04-07
通信作者: 牛红玲(1978-),女,讲师,主要从事分数阶微分方程数值解的研究.E-mail:g831020@126.com.
基金项目: 国家自然科学基金资助项目(11101282)
更新日期/Last Update: 2013-09-20