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 50 条

[21] Modified homotopy perturbation method for solving non-linear Fredholm integral equations
Javidi, M.
Golbabai, A.
CHAOS SOLITONS & FRACTALS, 2009, 40 (03) : 1408 - 1412
[22] Optimal homotopy asymptotic method for solving nonlinear Fredholm integral equations of second kind
Hashmi, M. S.
Khan, N.
Iqbal, S.
APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (22) : 10982 - 10989
[23] Optimal Homotopy Asymptotic Method for Solving the Linear Fredholm Integral Equations of the First Kind
Almousa, Mohammad
Ismail, Ahmad
ABSTRACT AND APPLIED ANALYSIS, 2013,
[24] New iterative method for solving linear and nonlinear hypersingular integral equations
Boykov, I. V.
Roudnev, V. A.
Boykova, A. I.
Baulina, O. A.
APPLIED NUMERICAL MATHEMATICS, 2018, 127 : 280 - 305
[25] Application of Optimal Homotopy Asymptotic Method for Solving Linear Delay Differential Equations
Anakira, N. Ratib
Alomari, A. K.
Hashim, I.
2013 UKM FST POSTGRADUATE COLLOQUIUM, 2013, 1571 : 1013 - 1019
[26] Application of homotopy-perturbation method to the second kind of nonlinear integral equations
Ganji, D. D.
Afrouzi, G. A.
Hosseinzadeh, H.
Talarposhti, R. A.
PHYSICS LETTERS A, 2007, 371 (1-2) : 20 - 25
[27] Convergence Analysis of Parabolic Basis Functions for Solving Systems of Linear and Nonlinear Fredholm Integral Equations
Jafarzadeh, Yousef
Keramati, Bagher
TURKISH JOURNAL OF MATHEMATICS, 2017, 41 (04) : 787 - 796
[28] Generalized homotopy method for solving nonlinear differential equations
Hector Vazquez-Leal
Computational and Applied Mathematics, 2014, 33 : 275 - 288
[29] Generalized homotopy method for solving nonlinear differential equations
Vazquez-Leal, Hector
COMPUTATIONAL & APPLIED MATHEMATICS, 2014, 33 (01): : 275 - 288
[30] A Numerical Algorithm for Solving Nonlinear Delay Volterra Integral Equations by Means of Homotopy Perturbation Method
Vanani, Solat Karimi
Yildirim, Ahmet
Soleymani, F.
Khan, M.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2011, 12 (1-8) : 15 - 21

← 1 2 3 4 5 →