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
收藏
页码：350 / 370
页数：21
相关论文
共 50 条
  • [1] Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind
    Edyta Hetmaniok
    Damian Słota
    Tomasz Trawiński
    Roman Wituła
    Numerical Algorithms, 2014, 67 : 163 - 185
  • [2] Usage of the homotopy analysis method for solving the nonlinear and linear integral equations of the second kind
    Hetmaniok, Edyta
    Slota, Damian
    Trawinski, Tomasz
    Witula, Roman
    NUMERICAL ALGORITHMS, 2014, 67 (01) : 163 - 185
  • [3] Solving linear and nonlinear Abel fuzzy integral equations by homotopy analysis method
    Mirzaee, Farshid
    Yari, Mohammad Komak
    Paripour, Mahmoud
    JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, 2015, 9 (01): : 104 - 115
  • [4] Application of Homotopy Analysis Method for Solving Systems of Volterra Integral Equations
    Matinfar, M.
    Saeidy, M.
    Vahidi, J.
    ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2012, 4 (01) : 36 - 45
  • [5] Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method
    Georgieva, Atanaska
    DEMONSTRATIO MATHEMATICA, 2021, 54 (01) : 11 - 24
  • [6] Convergence and error estimation of homotopy analysis method for some type of nonlinear and linear integral equations
    Hetmaniok, Edyta
    Nowak, Iwona
    Slota, Damian
    Witula, Roman
    JOURNAL OF NUMERICAL MATHEMATICS, 2015, 23 (04) : 331 - 344
  • [7] Multistage Homotopy Analysis Method for Solving Nonlinear Integral Equations
    Jafari, H.
    Firoozjaee, M. A.
    APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL, 2010, : 34 - 45
  • [8] Application of the homotopy analysis method to solving nonlinear evolution equations
    Shi, YR
    Xu, XJ
    Wu, ZX
    Wang, YH
    Yang, HJ
    Duan, WS
    Lü, KP
    ACTA PHYSICA SINICA, 2006, 55 (04) : 1555 - 1560
  • [9] ON A HOMOTOPY BASED METHOD FOR SOLVING SYSTEMS OF LINEAR EQUATIONS
    Saeidian, J.
    Babolian, E.
    Azizi, A.
    TWMS JOURNAL OF PURE AND APPLIED MATHEMATICS, 2015, 6 (01): : 15 - 26
  • [10] 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
12345