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A new approach to the trial function for Homotopy Perturbation Method for nonlinear problems

Year 2013, Volume: 1 Issue: 2, 1 - 10, 01.10.2013

Nalan Antar Nevin Pamuk

Abstract

In this paper, we give a new approach to the trial function for Homotopy Perturbation Method (HPM) which is powerful, easy-to-use and effective approximateanalytical mathematical tool. By generalizing of the trial function, we obtain betterapproximate series solutions for the linear or nonlinear problems, and we minimize thecomputational work and the time by choosing trial function properly

Keywords

Nonlinear differential equations homotopy perturbation method series solutions

References

  • C.Jin, M.Liu, A new modiŞcation of Adomian decomposition method for solving a kind of evolution equation, Applied Math.and Comp., 169(2005)953-962.
  • J.H.He, Homotopy perturbation technique, Comput.Methods Appl. Mech.Engrg 178(1999) 257-262.
  • S.J.Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D thesis, Shanghai Jiao tong University, (1992)
  • J.H.He, Homotopy perturbation method. A new nonlinear analytical Technique, Appl.Math.Comp. 135(2003)73-79.
  • N.Pamuk, Series Solution for Porous Medium Equation with a Source Term by Adomian’s Decomposition Method, Appl. Math.Comput.178(2006)480-485.
  • A.D. Polyanin, V.F Zaitsev, Handbook of Nonlinear Partial Differantial Equa- tions, Chapman and Hall/CRC Press, Boca Raton,(2004)
  • C. Gui and X. Kang, Localization for a Porous Medium type Equation in high dimensions, Transactions of the American mathmatical society 356(2004)4273-4285.
  • S.Pamuk, N.Pamuk, He’s Homotopy Perturbation Method for continuous pop- ulation models for single and interacting species, Comp. and Math. with applications 59(2010)612-621.
  • J.H. He, Homotopy Perturbation Method for Solving Boundary Value Problems, Physics Letters A 350(2006) 87-88.
  • J.H.He, Recent devolopment of the Homotopy perturbation method, Topolog- ical methods in nonlinear analysis, 31(2008)205-209.
  • J.H.He, New interpretation of Homotopy perturbation method, International journal of modern physics B, 20(18)(2006)2561-2568.
  • J.H.He, Application of Homotopy perturbation method to nonlinear wave equa- tions, Chaos solitons and fractals, 26(2005) 695-700.
  • Abbasbandy S, The application of Homotopy analysis method to nonlinear equations arising in heat transfer, Physics lett.A,360(2006) 109-13.
  • Liao SJ, On the Homotopy analysis method for nonlinear problems, Appl. math.comp., 147(2004)499-513.
  • Liao SJ, Numerically solving nonlinear problems by Homotopy analysis method, Comput.mech., 20(1997)530-40.
  • DD Ganji, Application of Homotopy perturbation and Variational iteration methods to nonlinear heat transfer and porous media equations, Journal of Comp. and appl. math., 207(2007)24-34.
  • M.Wang, X. Li and J Zhang, Phys.lett.A, (2008)372-417.
  • M.L. Wang, Physics Lett.A, (1996)213-219.
  • Z. Yubn, W. Mngliang and W. Yueming, Phys. lett. A,(2003)308-31.
  • M.H.M. Moussa and R.M. El Shikh, Physica A, (2006)371,325.
  • J.H.He and X.H.Wu, Chaos solitons and fractals, 30(2008)700.
  • J.H.He, Comparison of Homotopy perturbation method and homotopy analysis method, Applied Math. and comp.,156(2004) 527-539.
  • J.H.He, An elementary introduction to the homotopy perturbation method, Comp. and Math. with Appl., 57(2009)410-412.
  • S.Liang, D.J.Jeffrey, Comparison of homotopy analysis method and homotopy perturbation method through an evaluation equation, Commn nonlinear sci. numer. simulat., 14(2009)4057-4064. 10

A new approach to the trial function for Homotopy Perturbation Method for nonlinear problems

Year 2013, Volume: 1 Issue: 2, 1 - 10, 01.10.2013

Nalan Antar Nevin Pamuk

Abstract

In this paper, we give a new approach to the trial function for Homotopy Perturbation Method (HPM) which is powerful, easy-to-use and effective approximate
analytical mathematical tool. By generalizing of the trial function, we obtain better
approximate series solutions for the linear or nonlinear problems, and we minimize the
computational work and the time by choosing trial function properly.

Keywords

Nonlinear differential equations

References

  • C.Jin, M.Liu, A new modiŞcation of Adomian decomposition method for solving a kind of evolution equation, Applied Math.and Comp., 169(2005)953-962.
  • J.H.He, Homotopy perturbation technique, Comput.Methods Appl. Mech.Engrg 178(1999) 257-262.
  • S.J.Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D thesis, Shanghai Jiao tong University, (1992)
  • J.H.He, Homotopy perturbation method. A new nonlinear analytical Technique, Appl.Math.Comp. 135(2003)73-79.
  • N.Pamuk, Series Solution for Porous Medium Equation with a Source Term by Adomian’s Decomposition Method, Appl. Math.Comput.178(2006)480-485.
  • A.D. Polyanin, V.F Zaitsev, Handbook of Nonlinear Partial Differantial Equa- tions, Chapman and Hall/CRC Press, Boca Raton,(2004)
  • C. Gui and X. Kang, Localization for a Porous Medium type Equation in high dimensions, Transactions of the American mathmatical society 356(2004)4273-4285.
  • S.Pamuk, N.Pamuk, He’s Homotopy Perturbation Method for continuous pop- ulation models for single and interacting species, Comp. and Math. with applications 59(2010)612-621.
  • J.H. He, Homotopy Perturbation Method for Solving Boundary Value Problems, Physics Letters A 350(2006) 87-88.
  • J.H.He, Recent devolopment of the Homotopy perturbation method, Topolog- ical methods in nonlinear analysis, 31(2008)205-209.
  • J.H.He, New interpretation of Homotopy perturbation method, International journal of modern physics B, 20(18)(2006)2561-2568.
  • J.H.He, Application of Homotopy perturbation method to nonlinear wave equa- tions, Chaos solitons and fractals, 26(2005) 695-700.
  • Abbasbandy S, The application of Homotopy analysis method to nonlinear equations arising in heat transfer, Physics lett.A,360(2006) 109-13.
  • Liao SJ, On the Homotopy analysis method for nonlinear problems, Appl. math.comp., 147(2004)499-513.
  • Liao SJ, Numerically solving nonlinear problems by Homotopy analysis method, Comput.mech., 20(1997)530-40.
  • DD Ganji, Application of Homotopy perturbation and Variational iteration methods to nonlinear heat transfer and porous media equations, Journal of Comp. and appl. math., 207(2007)24-34.
  • M.Wang, X. Li and J Zhang, Phys.lett.A, (2008)372-417.
  • M.L. Wang, Physics Lett.A, (1996)213-219.
  • Z. Yubn, W. Mngliang and W. Yueming, Phys. lett. A,(2003)308-31.
  • M.H.M. Moussa and R.M. El Shikh, Physica A, (2006)371,325.
  • J.H.He and X.H.Wu, Chaos solitons and fractals, 30(2008)700.
  • J.H.He, Comparison of Homotopy perturbation method and homotopy analysis method, Applied Math. and comp.,156(2004) 527-539.
  • J.H.He, An elementary introduction to the homotopy perturbation method, Comp. and Math. with Appl., 57(2009)410-412.
  • S.Liang, D.J.Jeffrey, Comparison of homotopy analysis method and homotopy perturbation method through an evaluation equation, Commn nonlinear sci. numer. simulat., 14(2009)4057-4064. 10
There are 24 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Nalan Antar This is me

Nevin Pamuk This is me

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

Cite

APA Antar, N., & Pamuk, N. (2013). A new approach to the trial function for Homotopy Perturbation Method for nonlinear problems. Elektronik Mesleki Gelişim Ve Araştırmalar Dergisi, 1(2), 1-10.
AMA Antar N, Pamuk N. A new approach to the trial function for Homotopy Perturbation Method for nonlinear problems. Elektronik Mesleki Gelişim Ve Araştırmalar Dergisi. October 2013;1(2):1-10.
Chicago Antar, Nalan, and Nevin Pamuk. “A New Approach to the Trial Function for Homotopy Perturbation Method for Nonlinear Problems”. Elektronik Mesleki Gelişim Ve Araştırmalar Dergisi 1, no. 2 (October 2013): 1-10.
EndNote Antar N, Pamuk N (October 1, 2013) A new approach to the trial function for Homotopy Perturbation Method for nonlinear problems. Elektronik Mesleki Gelişim Ve Araştırmalar Dergisi 1 2 1–10.
IEEE N. Antar and N. Pamuk, “A new approach to the trial function for Homotopy Perturbation Method for nonlinear problems”, Elektronik Mesleki Gelişim Ve Araştırmalar Dergisi, vol. 1, no. 2, pp. 1–10, 2013.
ISNAD Antar, Nalan - Pamuk, Nevin. “A New Approach to the Trial Function for Homotopy Perturbation Method for Nonlinear Problems”. Elektronik Mesleki Gelişim Ve Araştırmalar Dergisi 1/2 (October 2013), 1-10.
JAMA Antar N, Pamuk N. A new approach to the trial function for Homotopy Perturbation Method for nonlinear problems. Elektronik Mesleki Gelişim Ve Araştırmalar Dergisi. 2013;1:1–10.
MLA Antar, Nalan and Nevin Pamuk. “A New Approach to the Trial Function for Homotopy Perturbation Method for Nonlinear Problems”. Elektronik Mesleki Gelişim Ve Araştırmalar Dergisi, vol. 1, no. 2, 2013, pp. 1-10.
Vancouver Antar N, Pamuk N. A new approach to the trial function for Homotopy Perturbation Method for nonlinear problems. Elektronik Mesleki Gelişim Ve Araştırmalar Dergisi. 2013;1(2):1-10.