A multiscale Galerkin method for second-order boundary value problems of Fredholm integro-differential equation

被引：24

作者：

Chen, Jian ^{[1
]}

Huang, Yong ^{[1
]}

Rong, Haiwu ^{[1
]}

Wu, Tingting ^{[2
]}

Zeng, Taishan ^{[3
]}

机构：

[1] Foshan Univ, Dept Math, Foshan 528000, Peoples R China

[2] Shangdong Normal Univ, Sch Math Sci, Jinan 250014, Peoples R China

[3] S China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2015年 / 290卷

关键词：

Multiscale Galerkin method; Multiscale othonormal bases; Boundary value problems; Fredholm integro-differential equation; MULTILEVEL AUGMENTATION METHODS; DIFFERENTIAL-EQUATIONS; OPERATOR-EQUATIONS; INTEGRAL-EQUATIONS; BANACH-SPACES;

D O I：

10.1016/j.cam.2015.06.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, multiscale Galerkin method is presented to approximate the solutions of second-order boundary value problems of Fredholm integro-differential equation. The method is based on traditional Galerkin method and uses the multiscale orthonormal bases to discretize the equations. The proposed method is proved to be stable and have the optimal convergence order. Numerical examples are presented to confirm the theoretical results and show that the method is computationally stable, valid and accurate. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：633 / 640

页数：8

共 25 条

[1]

[Anonymous], 2002, Int. J. Appl. Math.

[2] RETRACTED: Solution of nonlinear Fredholm integro-differential equations using a hybrid of block pulse functions and normalized Bernstein polynomials (Retracted Article) [J].

Behiry, S. H. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 260 :258-265

[3]

Behiry S.H., 2012, Natural Science, P581, DOI 0.4236/ns.2012.48077

[4] A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals [J].

Bhrawy, A. H. ;

Tohidi, E. ;

Soleymani, F. .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 219 (02) :482-497

[5] Fast multilevel augmentation method for nonlinear integral equations [J].

Chen, Jian .

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2012, 89 (01) :80-89

[6] Fast multilevel augmentation methods for nonlinear boundary value problems [J].

Chen, Jian .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (03) :612-619

[7] Multilevel augmentation methods for solving the sine-Gordon equation [J].

Chen, Jian ;

Chen, Zhongying ;

Cheng, Sirui .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 375 (02) :706-724

[8]

Chen M., 1997, APPROXIMATE SOLUTION

[9]

Chen Z., 2005, Num. Math. Jl. Chinese Univ, V14, P31

[10] FAST MULTILEVEL AUGMENTATION METHODS FOR SOLVING HAMMERSTEIN EQUATIONS [J].

Chen, Zhongying ;

Wu, Bin ;

Xu, Yuesheng .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (03) :2321-2346

← 1 2 3 →