메뉴 건너뛰기




Volumn 61, Issue 8, 2011, Pages 1963-1967

Homotopy perturbation transform method for nonlinear equations using He's polynomials

Author keywords

He's polynomials; Homotopy perturbation method; Laplace transform method; Nonlinear advection equations

Indexed keywords

ADOMIAN'S POLYNOMIALS; DECOMPOSITION METHODS; DISCRETIZATIONS; HE'S POLYNOMIALS; HOMOTOPIES; HOMOTOPY PERTURBATION METHOD; LAPLACE TRANSFORM METHOD; NONLINEAR ADVECTION EQUATION; NONLINEAR PROBLEMS; NONLINEAR TERMS; ROUND-OFF ERRORS; TRANSFORM METHODS;

EID: 79651475645     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2010.08.022     Document Type: Article
Times cited : (281)

References (49)
  • 3
    • 70350574745 scopus 로고    scopus 로고
    • Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method
    • N.H. Sweilam, and M.M. Khader Exact solutions of some coupled nonlinear partial differential equations using the homotopy perturbation method Computers & Mathematics with Applications 58 2009 2134 2141
    • (2009) Computers & Mathematics with Applications , vol.58 , pp. 2134-2141
    • Sweilam, N.H.1    Khader, M.M.2
  • 4
    • 70350572835 scopus 로고    scopus 로고
    • He's homotopy perturbation method: An effective tool for solving nonlinear integral and integro-differential equations
    • J. Saberi-Nadjafi, and A. Ghorbani He's homotopy perturbation method: an effective tool for solving nonlinear integral and integro-differential equations Computers & Mathematics with Applications 58 2009 1345 1351
    • (2009) Computers & Mathematics with Applications , vol.58 , pp. 1345-1351
    • Saberi-Nadjafi, J.1    Ghorbani, A.2
  • 6
    • 35949040541 scopus 로고
    • Exact solutions of the Kortewegde Vries equation for multiple collisions of solitons
    • R. Hirota Exact solutions of the Kortewegde Vries equation for multiple collisions of solitons Physical Review Letters 27 1971 1192 1194
    • (1971) Physical Review Letters , vol.27 , pp. 1192-1194
    • Hirota, R.1
  • 7
    • 77957929296 scopus 로고    scopus 로고
    • On multiple soliton solutions for coupled KdVmkdV equation
    • A.M. Wazwaz On multiple soliton solutions for coupled KdVmkdV equation Nonlinear Science Letters A 1 2010 289 296
    • (2010) Nonlinear Science Letters A , vol.1 , pp. 289-296
    • Wazwaz, A.M.1
  • 9
    • 77953478412 scopus 로고    scopus 로고
    • Fractional calculus of variations in fractal spacetime
    • G.C. Wu, and J.H. He Fractional calculus of variations in fractal spacetime Nonlinear Science Letters A 1 2010 281 287
    • (2010) Nonlinear Science Letters A , vol.1 , pp. 281-287
    • Wu, G.C.1    He, J.H.2
  • 10
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration methoda kind of nonlinear analytical technique: Some examples
    • J.H. He Variational iteration methoda kind of nonlinear analytical technique: some examples International Journal of Nonlinear Mechanics 34 1999 699 708
    • (1999) International Journal of Nonlinear Mechanics , vol.34 , pp. 699-708
    • He, J.H.1
  • 11
    • 34748870677 scopus 로고    scopus 로고
    • Variational iteration method: New development and applications
    • J.H. He, and X.H. Wu Variational iteration method: new development and applications Computers & Mathematics with Applications 54 2007 881 894
    • (2007) Computers & Mathematics with Applications , vol.54 , pp. 881-894
    • He, J.H.1    Wu, X.H.2
  • 12
    • 74449084990 scopus 로고    scopus 로고
    • The variational iteration method which should be followed
    • J.H. He, G.C. Wu, and F. Austin The variational iteration method which should be followed Nonlinear Science Letters A 1 2009 1 30
    • (2009) Nonlinear Science Letters A , vol.1 , pp. 1-30
    • He, J.H.1    Wu, G.C.2    Austin, F.3
  • 14
    • 79951849640 scopus 로고    scopus 로고
    • Analytical approach to two-dimensional viscous flow with a shrinking sheet via variational iteration algorithm-II
    • doi:10.1016/j.jksus.2010.06.010
    • N. Faraz, Y. Khan, A. Yildirim, Analytical approach to two-dimensional viscous flow with a shrinking sheet via variational iteration algorithm-II, Journal of King Saud University (2010) doi:10.1016/j.jksus.2010.06.010.
    • (2010) Journal of King Saud University
    • Faraz, N.1    Khan, Y.2    Yildirim, A.3
  • 15
    • 77953478991 scopus 로고    scopus 로고
    • Fractional variational iteration method and its application
    • 10.1016/j.physleta.2010.04.034
    • G.C. Wu, and E.W.M. Lee Fractional variational iteration method and its application Physics Letters A 2010 10.1016/j.physleta.2010.04.034
    • (2010) Physics Letters A
    • Wu, G.C.1    Lee, E.W.M.2
  • 17
    • 77950428340 scopus 로고    scopus 로고
    • Fourier-series-based variational iteration method for a reliable treatment of heat equations with variable coefficients
    • C. Chun Fourier-series-based variational iteration method for a reliable treatment of heat equations with variable coefficients International Journal of Nonlinear Sciences and Numerical Simulation 10 2009 1383 1388
    • (2009) International Journal of Nonlinear Sciences and Numerical Simulation , vol.10 , pp. 1383-1388
    • Chun, C.1
  • 19
    • 34250650488 scopus 로고    scopus 로고
    • A comparison between the variational iteration method and adomian decomposition method
    • A.M. Wazwaz A comparison between the variational iteration method and adomian decomposition method Journal of Computational and Applied Mathematics 207 2007 129 136
    • (2007) Journal of Computational and Applied Mathematics , vol.207 , pp. 129-136
    • Wazwaz, A.M.1
  • 20
    • 27144467065 scopus 로고    scopus 로고
    • New applications of variational iteration method
    • DOI 10.1016/j.physd.2005.08.002, PII S0167278905003337
    • M.A. Abdou, and A.A. Soliman New applications of variational iteration method Physica D: Nonlinear Phenomena 211 2005 1 8 (Pubitemid 41491773)
    • (2005) Physica D: Nonlinear Phenomena , vol.211 , Issue.1-2 , pp. 1-8
    • Abdou, M.A.1    Soliman, A.A.2
  • 21
    • 0141961669 scopus 로고    scopus 로고
    • Weighted finite difference techniques for the one-dimensional advectiondiffusion equation
    • M. Dehghan Weighted finite difference techniques for the one-dimensional advectiondiffusion equation Applied Mathematics and Computation 147 2004 307 319
    • (2004) Applied Mathematics and Computation , vol.147 , pp. 307-319
    • Dehghan, M.1
  • 22
    • 33748919061 scopus 로고    scopus 로고
    • Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations
    • D.D. Ganji, and A. Sadighi Application of He's homotopy perturbation method to nonlinear coupled systems of reaction diffusion equations International Journal of Nonlinear Sciences and Numerical Simulation 7 2006 411 418 (Pubitemid 44433692)
    • (2006) International Journal of Nonlinear Sciences and Numerical Simulation , vol.7 , Issue.4 , pp. 411-418
    • Ganji, D.D.1    Sadighi, A.2
  • 23
    • 77958170006 scopus 로고    scopus 로고
    • Application of the Laplace decomposition method to nonlinear homogeneous and non-homogenous advection equations
    • Y. Khan, and F. Austin Application of the Laplace decomposition method to nonlinear homogeneous and non-homogenous advection equations Zeitschrift fuer Naturforschung 65a 2010 1 5
    • (2010) Zeitschrift fuer Naturforschung , vol.65 , pp. 1-5
    • Khan, Y.1    Austin, F.2
  • 24
  • 25
    • 0037440579 scopus 로고    scopus 로고
    • Homotopy perturbation method: A new nonlinear analytical technique
    • J.H. He Homotopy perturbation method: a new nonlinear analytical technique Applied Mathematics and Computation 135 2003 73 79
    • (2003) Applied Mathematics and Computation , vol.135 , pp. 73-79
    • He, J.H.1
  • 26
    • 3943092529 scopus 로고    scopus 로고
    • Comparison of homotopy perturbation method and homotopy analysis method
    • J.H. He Comparison of homotopy perturbation method and homotopy analysis method Applied Mathematics and Computation 156 2004 527 539
    • (2004) Applied Mathematics and Computation , vol.156 , pp. 527-539
    • He, J.H.1
  • 27
    • 1242287587 scopus 로고    scopus 로고
    • The homotopy perturbation method for nonlinear oscillators with discontinuities
    • J.H. He The homotopy perturbation method for nonlinear oscillators with discontinuities Applied Mathematics and Computation 151 2004 287 292
    • (2004) Applied Mathematics and Computation , vol.151 , pp. 287-292
    • He, J.H.1
  • 29
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equation
    • J.H. He Some asymptotic methods for strongly nonlinear equation International Journal of Modern Physics 20 2006 1144 1199
    • (2006) International Journal of Modern Physics , vol.20 , pp. 1144-1199
    • He, J.H.1
  • 30
    • 30644460357 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving boundary value problems
    • J.H. He Homotopy perturbation method for solving boundary value problems Physics Letters A 350 2006 87 88
    • (2006) Physics Letters A , vol.350 , pp. 87-88
    • He, J.H.1
  • 31
    • 33745965279 scopus 로고    scopus 로고
    • Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method
    • M. Rafei, and D.D. Ganji Explicit solutions of helmhotz equation and fifth-order KdV equation using homotopy perturbation method International Journal of Nonlinear Sciences and Numerical Simulation 7 2006 321 328 (Pubitemid 44059427)
    • (2006) International Journal of Nonlinear Sciences and Numerical Simulation , vol.7 , Issue.3 , pp. 321-328
    • Rafei, M.1    Ganji, D.D.2
  • 33
    • 33646893481 scopus 로고    scopus 로고
    • The applications of He's homotopy perturbation method to nonlinear equation arising in heat transfer
    • D.D. Ganji The applications of He's homotopy perturbation method to nonlinear equation arising in heat transfer Physics Letters A 335 2006 337 3341
    • (2006) Physics Letters A , vol.335 , pp. 337-3341
    • Ganji, D.D.1
  • 34
    • 34748871953 scopus 로고    scopus 로고
    • He's homotopy perturbation method for a boundary layer equation in unbounded domain
    • DOI 10.1016/j.camwa.2006.12.052, PII S0898122107002787, Variational Iteration Method for Nonlinear Problems
    • L. Xu He's homotopy perturbation method for a boundary layer equation in unbounded domain Computers & Mathematics with Applications 54 2007 1067 1070 (Pubitemid 47488822)
    • (2007) Computers and Mathematics with Applications , vol.54 , Issue.7-8 , pp. 1067-1070
    • Xu, L.1
  • 35
    • 50949112266 scopus 로고    scopus 로고
    • An elementary introduction of recently developed asymptotic methods and nanomechanics in textile engineering
    • J.H. He An elementary introduction of recently developed asymptotic methods and nanomechanics in textile engineering International Journal of Modern Physics 22 2008 3487 4578
    • (2008) International Journal of Modern Physics , vol.22 , pp. 3487-4578
    • He, J.H.1
  • 36
    • 50949124409 scopus 로고    scopus 로고
    • Recent developments of the homotopy perturbation method
    • J.H. He Recent developments of the homotopy perturbation method Topological Methods in Nonlinear Analysis 31 2008 205 209
    • (2008) Topological Methods in Nonlinear Analysis , vol.31 , pp. 205-209
    • He, J.H.1
  • 39
    • 72949083989 scopus 로고    scopus 로고
    • Extracting a general iterative method from an adomian decomposition method and comparing it to the variational iteration method
    • J. Biazar, M. Gholami Porshokuhi, and B. Ghanbari Extracting a general iterative method from an adomian decomposition method and comparing it to the variational iteration method Computers & Mathematics with Applications 59 2010 622 628
    • (2010) Computers & Mathematics with Applications , vol.59 , pp. 622-628
    • Biazar, J.1    Gholami Porshokuhi, M.2    Ghanbari, B.3
  • 40
    • 33744989624 scopus 로고    scopus 로고
    • A Laplace decomposition algorithm applied to a class of nonlinear differential equations
    • S.A. Khuri A Laplace decomposition algorithm applied to a class of nonlinear differential equations Journal of Applied Mathematics 1 2001 141 155
    • (2001) Journal of Applied Mathematics , vol.1 , pp. 141-155
    • Khuri, S.A.1
  • 41
    • 33744969617 scopus 로고    scopus 로고
    • Numerical solution of Duffing equation by the Laplace decomposition algorithm
    • E. Yusufoglu Numerical solution of Duffing equation by the Laplace decomposition algorithm Applied Mathematics and Computation 177 2006 572 580
    • (2006) Applied Mathematics and Computation , vol.177 , pp. 572-580
    • Yusufoglu, E.1
  • 42
    • 77950456001 scopus 로고    scopus 로고
    • An effective modification of the Laplace decomposition method for nonlinear equations
    • Yasir Khan An effective modification of the Laplace decomposition method for nonlinear equations International Journal of Nonlinear Sciences and Numerical Simulation 10 2009 1373 1376
    • (2009) International Journal of Nonlinear Sciences and Numerical Simulation , vol.10 , pp. 1373-1376
    • Khan, Y.1
  • 44
    • 79951850451 scopus 로고    scopus 로고
    • Numerical solution of logistic differential equations by using the Laplace decomposition method
    • S. Islam, Y. Khan, N. Faraz, and F. Austin Numerical solution of logistic differential equations by using the Laplace decomposition method World Applied Sciences Journal 8 2010 1100 1105
    • (2010) World Applied Sciences Journal , vol.8 , pp. 1100-1105
    • Islam, S.1    Khan, Y.2    Faraz, N.3    Austin, F.4
  • 45
    • 79951684448 scopus 로고    scopus 로고
    • Homotopy perturbation algorithm using Laplace transformation
    • M. Madani, and M. Fathizadeh Homotopy perturbation algorithm using Laplace transformation Nonlinear Science Letters A 1 2010 263 267
    • (2010) Nonlinear Science Letters A , vol.1 , pp. 263-267
    • Madani, M.1    Fathizadeh, M.2
  • 46
    • 47649131065 scopus 로고    scopus 로고
    • Variational homotopy perturbation method for solving higher dimensional initial boundary value problems
    • Article ID 696734, doi:10.1155/2008/696734
    • M.A. Noor, S.T. Mohyud-Din, Variational homotopy perturbation method for solving higher dimensional initial boundary value problems, Mathematical Problems in Engineering 2008 (2008) 11. Article ID 696734, doi:10.1155/2008/ 696734.
    • (2008) Mathematical Problems in Engineering 2008 , vol.11
    • Noor, M.A.1    Mohyud-Din, S.T.2
  • 48
    • 62949242120 scopus 로고    scopus 로고
    • Beyond adomian's polynomials: He polynomials
    • A. Ghorbani Beyond adomian's polynomials: He polynomials Chaos Solitons Fractals 39 2009 1486 1492
    • (2009) Chaos Solitons Fractals , vol.39 , pp. 1486-1492
    • Ghorbani, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.