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

Year 2013, Volume: 1 Issue: 2, 22 - 26, 01.08.2013

Hossein Jafari Maryam Ghorbani Saber Ghasempour

Abstract

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

Keywords

Modified Homotopy perturbation method nonlinear integral equations; series solution method

References

  • 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

Year 2013, Volume: 1 Issue: 2, 22 - 26, 01.08.2013

Hossein Jafari Maryam Ghorbani Saber Ghasempour

Abstract

References

  • 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.
There are 9 citations in total.

Details

Journal Section Articles
Authors

Hossein Jafari This is me

Maryam Ghorbani This is me

Saber Ghasempour This is me

Publication Date August 1, 2013
Published in Issue Year 2013 Volume: 1 Issue: 2

Cite

APA Jafari, H., Ghorbani, M., & Ghasempour, S. (2013). 2 The Principle of the New Modification of the Homotopy Perturbation Method. New Trends in Mathematical Sciences, 1(2), 22-26.
AMA Jafari H, Ghorbani M, Ghasempour S. 2 The Principle of the New Modification of the Homotopy Perturbation Method. New Trends in Mathematical Sciences. August 2013;1(2):22-26.
Chicago Jafari, Hossein, Maryam Ghorbani, and Saber Ghasempour. “2 The Principle of the New Modification of the Homotopy Perturbation Method”. New Trends in Mathematical Sciences 1, no. 2 (August 2013): 22-26.
EndNote Jafari H, Ghorbani M, Ghasempour S (August 1, 2013) 2 The Principle of the New Modification of the Homotopy Perturbation Method. New Trends in Mathematical Sciences 1 2 22–26.
IEEE H. Jafari, M. Ghorbani, and S. Ghasempour, “2 The Principle of the New Modification of the Homotopy Perturbation Method”, New Trends in Mathematical Sciences, vol. 1, no. 2, pp. 22–26, 2013.
ISNAD Jafari, Hossein et al. “2 The Principle of the New Modification of the Homotopy Perturbation Method”. New Trends in Mathematical Sciences 1/2 (August 2013), 22-26.
JAMA Jafari H, Ghorbani M, Ghasempour S. 2 The Principle of the New Modification of the Homotopy Perturbation Method. New Trends in Mathematical Sciences. 2013;1:22–26.
MLA Jafari, Hossein et al. “2 The Principle of the New Modification of the Homotopy Perturbation Method”. New Trends in Mathematical Sciences, vol. 1, no. 2, 2013, pp. 22-26.
Vancouver Jafari H, Ghorbani M, Ghasempour S. 2 The Principle of the New Modification of the Homotopy Perturbation Method. New Trends in Mathematical Sciences. 2013;1(2):22-6.