BibTex RIS Kaynak Göster

A note on exact solutions for nonlinear integral equations by a modified homotopy perturbation method

Yıl 2013, Cilt: 1 Sayı: 2, 22 - 26, 01.08.2013

Hossein Jafari Maryam Ghorbani Saber Ghasempour

Öz

In the paper "Exact solutions for nonlinear integral equations by a modified homotopy perturbation method" by A. Ghorbani and J. Saberi-Nadjafi, Computers and Mathematics with Applications, 56, (2008) 1032-1039, the authors introduced a new modification of the homotopy perturbation method to solve nonlinear integral equations.We discuss here the restrictions on their method for solving nonlinear integral equations. We also prove analytically that the method given by Ghorbani and Saberi-Nadjafi is equivalent to the series solution method when selective functions are polynomials

Anahtar Kelimeler

Modified Homotopy perturbation method nonlinear integral equations; series solution method

Kaynakça

  • Ghorbani, J. Saberi-Nadjafi, Exact solutions for nonlinear integral equations by a modified homotopy perturbation method,Computers and Mathematics with Applications 56 (2008) 1032-1039.
  • G. Adomian, Y. Cherruault, K. Abbaoui, A Nonperturbative Analytical Solution of Immune Response with Time-Delays and Possible Generalization, Mathl. Comput. Modelling Vol. 24(10) (1996) 89–96.
  • A. Ghorbani, Beyond Adomian polynomials: He polynomials, Chaos Solitons and Fractals, 39 (2009) 1486–1492.
  • J.H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Non- Linear Mechanics 35(1) (2000) 37–43.
  • J.H. He, New Interpretation of homotopy-perturbation method, Int. J. Mod. Phys. B, 20 (18) (2006): 2561–2568.
  • H. Jafari, S. Momani, Solving fractional diffusion and wave equations by modified homotopy perturbation method, Physics Letters A, 370 (2007) 388–396.
  • H. Jafari, S. Ghasempoor, C. M. Khalique, A Comparison between Adomian Polynomials and He Polynomials for Nonlinear Functional Equations, Mathematical Problems in Engineering, Volume 2013 (2013), Article ID 943232, 4 pages.
  • A.M. Wazwaz, A First Course in Integral Equations, World Scientific, New Jersey, 1997.
  • A.M. Wazwaz, Linear and Nonlinear Integral Equations: Methods and Applications, Springer; 1st Edition 2011.

2 The Principle of the New Modification of the Homotopy Perturbation Method

Yıl 2013, Cilt: 1 Sayı: 2, 22 - 26, 01.08.2013

Hossein Jafari Maryam Ghorbani Saber Ghasempour

Öz

Kaynakça

  • Ghorbani, J. Saberi-Nadjafi, Exact solutions for nonlinear integral equations by a modified homotopy perturbation method,Computers and Mathematics with Applications 56 (2008) 1032-1039.
  • G. Adomian, Y. Cherruault, K. Abbaoui, A Nonperturbative Analytical Solution of Immune Response with Time-Delays and Possible Generalization, Mathl. Comput. Modelling Vol. 24(10) (1996) 89–96.
  • A. Ghorbani, Beyond Adomian polynomials: He polynomials, Chaos Solitons and Fractals, 39 (2009) 1486–1492.
  • J.H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, International Journal of Non- Linear Mechanics 35(1) (2000) 37–43.
  • J.H. He, New Interpretation of homotopy-perturbation method, Int. J. Mod. Phys. B, 20 (18) (2006): 2561–2568.
  • H. Jafari, S. Momani, Solving fractional diffusion and wave equations by modified homotopy perturbation method, Physics Letters A, 370 (2007) 388–396.
  • H. Jafari, S. Ghasempoor, C. M. Khalique, A Comparison between Adomian Polynomials and He Polynomials for Nonlinear Functional Equations, Mathematical Problems in Engineering, Volume 2013 (2013), Article ID 943232, 4 pages.
  • A.M. Wazwaz, A First Course in Integral Equations, World Scientific, New Jersey, 1997.
  • A.M. Wazwaz, Linear and Nonlinear Integral Equations: Methods and Applications, Springer; 1st Edition 2011.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Bölüm Articles
Yazarlar

Hossein Jafari Bu kişi benim

Maryam Ghorbani Bu kişi benim

Saber Ghasempour Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 1 Sayı: 2

Kaynak Göster

APA Jafari, H., Ghorbani, M., & Ghasempour, S. (2013). A note on exact solutions for nonlinear integral equations by a modified homotopy perturbation method. New Trends in Mathematical Sciences, 1(2), 22-26.
AMA Jafari H, Ghorbani M, Ghasempour S. A note on exact solutions for nonlinear integral equations by a modified homotopy perturbation method. New Trends in Mathematical Sciences. Ağustos 2013;1(2):22-26.
Chicago Jafari, Hossein, Maryam Ghorbani, ve Saber Ghasempour. “A Note on Exact Solutions for Nonlinear Integral Equations by a modified Homotopy Perturbation Method”. New Trends in Mathematical Sciences 1, sy. 2 (Ağustos 2013): 22-26.
EndNote Jafari H, Ghorbani M, Ghasempour S (01 Ağustos 2013) A note on exact solutions for nonlinear integral equations by a modified homotopy perturbation method. New Trends in Mathematical Sciences 1 2 22–26.
IEEE H. Jafari, M. Ghorbani, ve S. Ghasempour, “A note on exact solutions for nonlinear integral equations by a modified homotopy perturbation method”, New Trends in Mathematical Sciences, c. 1, sy. 2, ss. 22–26, 2013.
ISNAD Jafari, Hossein vd. “A Note on Exact Solutions for Nonlinear Integral Equations by a modified Homotopy Perturbation Method”. New Trends in Mathematical Sciences 1/2 (Ağustos 2013), 22-26.
JAMA Jafari H, Ghorbani M, Ghasempour S. A note on exact solutions for nonlinear integral equations by a modified homotopy perturbation method. New Trends in Mathematical Sciences. 2013;1:22–26.
MLA Jafari, Hossein vd. “A Note on Exact Solutions for Nonlinear Integral Equations by a modified Homotopy Perturbation Method”. New Trends in Mathematical Sciences, c. 1, sy. 2, 2013, ss. 22-26.
Vancouver Jafari H, Ghorbani M, Ghasempour S. A note on exact solutions for nonlinear integral equations by a modified homotopy perturbation method. New Trends in Mathematical Sciences. 2013;1(2):22-6.