Application of the Homotopy Analysis Method for Solving the Systems of Linear and Nonlinear Integral Equations

被引：3

作者：

Brociek, Rafal ^{[1
]}

Hetmaniok, Edyta ^{[1
]}

Matlak, Jaroslaw ^{[1
]}

Slota, Damian ^{[1
]}

机构：

[1] Silesian Tech Univ, Inst Math, Kaszubska 23, PL-44100 Gliwice, Poland

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2016年 / 21卷 / 03期

关键词：

homotopy analysis method; convergence; error estimation; system of Fredholm integral equations; system of Volterra integral equations; ANALYTIC METHOD; CONVERGENCE;

D O I：

10.3846/13926292.2016.1167787

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we indicate some applications of homotopy analysis method for solving the systems of linear and nonlinear integral equations. The method is based on the concept of creating function series. If the series converges, its sum is the solution of this system of equations. The paper presents conditions to ensure the convergence of this series and estimation of the error of approximate solution obtained when the partial sum of the series is used. Application of the method will be illustrated by examples.

引用

页码：350 / 370

页数：21

共 26 条

[1] A new analytical technique to solve Fredholm's integral equations [J].

Abbasbandy, Saeid ;

Shivanian, E. .

NUMERICAL ALGORITHMS, 2011, 56 (01) :27-43

[2]

Afroozi G., 2010, INT J NONLINEAR SCI, V9, P213

[3] Magnetohydrodynamic flow of a viscoelastic fluid [J].

Akyildiz, F. Talay ;

Vajravelu, K. .

PHYSICS LETTERS A, 2008, 372 (19) :3380-3384

[4]

[Anonymous], 1990, Topics in metric fixed point theory

[5]

Awawdeh F., 2009, INT MATH FORUM, V4, P805

[6]

Bazrafshan F., 2011, J KING SAUD UNIV SCI, V23, P111, DOI DOI 10.1016/j.jksus.2010.06.017

[7]

Behzadi Sh. Sadigh, 2011, J FUZZY SET VALUED A, V35, P1, DOI 10.5899/2011/

[8] CONVERGENCE OF ADOMIAN METHOD [J].

CHERRUAULT, Y .

KYBERNETES, 1989, 18 (02) :31-38

[9] Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations [J].

Hetmaniok, Edyta ;

Nowak, Iwona ;

Slota, Damian ;

Witula, Roman .

JOURNAL OF NUMERICAL MATHEMATICS, 2015, 23 (04) :331-344

[10] Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind [J].

Hetmaniok, Edyta ;

Slota, Damian ;

Trawinski, Tomasz ;

Witula, Roman .

NUMERICAL ALGORITHMS, 2014, 67 (01) :163-185

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