Homotopy perturbation method for the hypersingular integral equations of the first kind

被引：4
|
作者：
Eshkuvatov, Zainidin K. [1 ]
Zulkarnain, Fatimah Samihah [2 ]
Long, Nik Mohd Asri Nik [2 ]
Muminov, Zahriddin [3 ]
机构：
[1] USIM, Fac Sci & Technol, Nilai, Negeri Sembilan, Malaysia
[2] Univ Putra Malaysia, Fac Sci, Dept Math, Serdang, Selangor, Malaysia
[3] Nilai Univ, Fac Sci & Technol, Nilai, Negeri Sembilan, Malaysia
来源：
AIN SHAMS ENGINEERING JOURNAL | 2018年 / 9卷 / 04期
关键词：
Homotopy perturbation method; Hypersingular integral; Numerical method; Convergence; APPROXIMATE SOLUTION; CONVERGENCE; SCATTERING;
D O I：
10.1016/j.asej.2017.04.010
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
Simple and efficient convex homotopy perturbation method (HPM) is presented to obtain an approximate solution of hyper-singular integral equations of the first kind. Convergence and error estimate of HPM are obtained. Three numerical examples were provided to verify the effectiveness of the HPM. Comparisons with reproducing kernel method (Chen et al., 2011) for the same number of iteration is also presented. Numerical examples reveal that the convergence of HPM can still be achieved for some problems even if the condition of convergence of HPM is not satisfied. (C) 2017 Ain Shams University.
引用
收藏
页码：3359 / 3363
页数：5
相关论文
共 50 条
  • [1] Modified homotopy perturbation method for solving hypersingular integral equations of the first kind
    Eshkuvatov, Z. K.
    Zulkarnain, F. S.
    Long, N. M. A. Nik
    Muminov, Z.
    [J]. SPRINGERPLUS, 2016, 5
  • [2] Modified Homotopy Perturbation Method for Solving Hypersingular Integral Equations of the Second Kind
    Zulkarnain, F. S.
    Eshkuvatov, Z. K.
    Long, N. M. A. Nik
    Ismail, F.
    [J]. INNOVATIONS THROUGH MATHEMATICAL AND STATISTICAL RESEARCH: PROCEEDINGS OF THE 2ND INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS (ICMSS2016), 2016, 1739
  • [3] Hypersingular integral equations of the first kind: A modified homotopy perturbation method and its application to vibration and active control
    Novin, Reza
    Araghi, Mohammad Ali Fariborzi
    [J]. JOURNAL OF LOW FREQUENCY NOISE VIBRATION AND ACTIVE CONTROL, 2019, 38 (02) : 706 - 727
  • [4] Application of homotopy perturbation method for systems of Volterra integral equations of the first kind
    Biazar, J.
    Eslami, M.
    Aminikhah, H.
    [J]. CHAOS SOLITONS & FRACTALS, 2009, 42 (05) : 3020 - 3026
  • [5] A new method for solving hypersingular integral equations of the first kind
    Chen, Zhong
    Zhou, YongFang
    [J]. APPLIED MATHEMATICS LETTERS, 2011, 24 (05) : 636 - 641
  • [6] HOMOTOPY PERTURBATION METHOD AND CHEBYSHEV POLYNOMIALS FOR SOLVING A CLASS OF SINGULAR AND HYPERSINGULAR INTEGRAL EQUATIONS
    Eshkuvatov, Zainidin
    [J]. NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION, 2018, 8 (03): : 337 - 350
  • [7] Application of homotopy-perturbation method to the second kind of nonlinear integral equations
    Ganji, D. D.
    Afrouzi, G. A.
    Hosseinzadeh, H.
    Talarposhti, R. A.
    [J]. PHYSICS LETTERS A, 2007, 371 (1-2) : 20 - 25
  • [8] Study of convergence of Homotopy perturbation method for two-dimensional linear Volterra integral equations of the first kind
    Eslami, Mostafa
    Mirzazadeh, M.
    [J]. INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS, 2014, 5 (01) : 72 - 80
  • [9] Solution of non-linear Fredholm integral equations of the first kind using modified homotopy perturbation method
    Golbabai, A.
    Keramati, B.
    [J]. CHAOS SOLITONS & FRACTALS, 2009, 39 (05) : 2316 - 2321
  • [10] HOMOTOPY REGULARIZATION METHOD TO SOLVE THE SINGULAR VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND
    Araghi, Mohammad Ali Fariborzi
    Noeiaghdam, Samad
    [J]. JORDAN JOURNAL OF MATHEMATICS AND STATISTICS, 2018, 11 (01): : 1 - 12
12345