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Volumn 50, Issue 1-2, 2009, Pages 213-224

Some notes on using the homotopy perturbation method for solving time-dependent differential equations

Author keywords

Cauchy reaction diffusion equations; Emden Fowler equations; Evolution equations; Homotopy perturbation method; Klein Gordon equations

Indexed keywords

CAUCHY REACTION-DIFFUSION EQUATIONS; EMDEN-FOWLER EQUATIONS; EVOLUTION EQUATIONS; HOMOTOPY PERTURBATION METHOD; KLEIN-GORDON EQUATIONS;

EID: 67349210701     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2009.03.003     Document Type: Article
Times cited : (69)

References (29)
  • 1
    • 0032672778 scopus 로고    scopus 로고
    • Homotopy perturbation technique
    • He J.H. Homotopy perturbation technique. Comp. Meth. Appl. Mech. Eng. 178 (1999) 257-262
    • (1999) Comp. Meth. Appl. Mech. Eng. , vol.178 , pp. 257-262
    • He, J.H.1
  • 2
    • 0033702384 scopus 로고    scopus 로고
    • A coupling method of homotopy technique and a perturbation technique for non linear problems
    • He J.H. A coupling method of homotopy technique and a perturbation technique for non linear problems. Int. J. Non linear Mech. 35 (2000) 37-43
    • (2000) Int. J. Non linear Mech. , vol.35 , pp. 37-43
    • He, J.H.1
  • 3
    • 0037440579 scopus 로고    scopus 로고
    • Homotopy perturbation method: A new nonlinear analytical technique
    • He J.H. Homotopy perturbation method: A new nonlinear analytical technique. Appl. Math. Comput. 135 (2003) 73-79
    • (2003) Appl. Math. Comput. , vol.135 , pp. 73-79
    • He, J.H.1
  • 4
    • 0037431567 scopus 로고    scopus 로고
    • A simple perturbation approach to Blasius equation
    • He J.H. A simple perturbation approach to Blasius equation. Appl. Math. Comput. 140 (2003) 217-222
    • (2003) Appl. Math. Comput. , vol.140 , pp. 217-222
    • He, J.H.1
  • 5
    • 18844426016 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to nonlinear wave equations
    • He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos Solitons Fractals 26 (2005) 295-700
    • (2005) Chaos Solitons Fractals , vol.26 , pp. 295-700
    • He, J.H.1
  • 6
    • 30644460357 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving boundary value problems
    • He J.H. Homotopy perturbation method for solving boundary value problems. Phys. Lett. A 350 (2006) 87-88
    • (2006) Phys. Lett. A , vol.350 , pp. 87-88
    • He, J.H.1
  • 7
    • 55649112486 scopus 로고    scopus 로고
    • Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method
    • Yi{dotless}ldi{dotless}ri{dotless}m A. Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method. Comput. Math. Appl. 56 12 (2008) 3175-3180
    • (2008) Comput. Math. Appl. , vol.56 , Issue.12 , pp. 3175-3180
    • Yildirim, A.1
  • 8
    • 31144479330 scopus 로고    scopus 로고
    • Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method
    • Abbasbandy S. Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method. Appl. Math. Comput. 172 (2006) 485-490
    • (2006) Appl. Math. Comput. , vol.172 , pp. 485-490
    • Abbasbandy, S.1
  • 9
    • 41249090165 scopus 로고    scopus 로고
    • Modified homotopy perturbation method for solving Fredholm integral equations
    • Golbabai A., and Keramati B. Modified homotopy perturbation method for solving Fredholm integral equations. Chaos Solitons Fractals 37 5 (2008) 1528-1537
    • (2008) Chaos Solitons Fractals , vol.37 , Issue.5 , pp. 1528-1537
    • Golbabai, A.1    Keramati, B.2
  • 10
    • 34248227820 scopus 로고    scopus 로고
    • Numerical solutions of nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method
    • Ghasemi M., Tavassoli Kajani M., and Babolian E. Numerical solutions of nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method. Appl. Math. Comput. 188 (2007) 446-449
    • (2007) Appl. Math. Comput. , vol.188 , pp. 446-449
    • Ghasemi, M.1    Tavassoli Kajani, M.2    Babolian, E.3
  • 11
    • 62749090990 scopus 로고    scopus 로고
    • He's homotopy perturbation method for solving systems of Volterra integral equations
    • 10.1016/j.chaos.2007.01.108
    • Biazar J., and Ghazvini H. He's homotopy perturbation method for solving systems of Volterra integral equations. Chaos Solitons Fractals (2007) 10.1016/j.chaos.2007.01.108
    • (2007) Chaos Solitons Fractals
    • Biazar, J.1    Ghazvini, H.2
  • 12
    • 34247366852 scopus 로고    scopus 로고
    • A reliable treatment of homotopy perturbation method for Klein-Gordon equations
    • Odibat Z., and Momani S. A reliable treatment of homotopy perturbation method for Klein-Gordon equations. Phys. Lett. A 365 (2007) 351-357
    • (2007) Phys. Lett. A , vol.365 , pp. 351-357
    • Odibat, Z.1    Momani, S.2
  • 13
    • 63449096068 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to Klein-Gordon and sine-Gordon equations
    • 10.1016/j.chaos.2007.06.091
    • Chowdhury M.S.H., and Hashim I. Application of homotopy perturbation method to Klein-Gordon and sine-Gordon equations. Chaos Solitons Fractals (2007) 10.1016/j.chaos.2007.06.091
    • (2007) Chaos Solitons Fractals
    • Chowdhury, M.S.H.1    Hashim, I.2
  • 14
    • 34247347840 scopus 로고    scopus 로고
    • Solutions of class of singular second-order IVPs by homotopy perturbation method
    • Chowdhury M.S.H., and Hashim I. Solutions of class of singular second-order IVPs by homotopy perturbation method. Phys. Lett. A 365 (2007) 439-447
    • (2007) Phys. Lett. A , vol.365 , pp. 439-447
    • Chowdhury, M.S.H.1    Hashim, I.2
  • 15
    • 41949112904 scopus 로고    scopus 로고
    • Application of homotopy perturbation method to fractional IVPs
    • Abdul Aziz O., Hashim I., and Momani S. Application of homotopy perturbation method to fractional IVPs. J. Comput. Appl. Math. 216 2 (2008) 574-584
    • (2008) J. Comput. Appl. Math. , vol.216 , Issue.2 , pp. 574-584
    • Abdul Aziz, O.1    Hashim, I.2    Momani, S.3
  • 16
    • 34247862175 scopus 로고    scopus 로고
    • Exact solution of nonlinear Schrödinger equations by He's homotopy perturbation method
    • Biazar J., and Ghazvini H. Exact solution of nonlinear Schrödinger equations by He's homotopy perturbation method. Phys. Lett. A 366 (2007) 79-84
    • (2007) Phys. Lett. A , vol.366 , pp. 79-84
    • Biazar, J.1    Ghazvini, H.2
  • 17
    • 34547659368 scopus 로고    scopus 로고
    • Solutions of time-dependent Emden-Fowler type equations by homotopy perturbation method
    • Chowdhury M.S.H., and Hashim I. Solutions of time-dependent Emden-Fowler type equations by homotopy perturbation method. Phys. Lett. A 368 (2007) 305-313
    • (2007) Phys. Lett. A , vol.368 , pp. 305-313
    • Chowdhury, M.S.H.1    Hashim, I.2
  • 18
    • 34748815591 scopus 로고    scopus 로고
    • Variational iteration method and homotopy perturbation method for nonlinear evolution equations
    • Ganji D.D., Tari H., and Bakhshi Jooybari M. Variational iteration method and homotopy perturbation method for nonlinear evolution equations. Int. J. Comput. Math. Appl. 54 (2007) 1018-1027
    • (2007) Int. J. Comput. Math. Appl. , vol.54 , pp. 1018-1027
    • Ganji, D.D.1    Tari, H.2    Bakhshi Jooybari, M.3
  • 19
    • 77952576056 scopus 로고    scopus 로고
    • He's Homotopy Perturbation Method for nonlinear differential-difference equations
    • 10.1080/00207160802247646
    • Yi{dotless}ldi{dotless}ri{dotless}m A. He's Homotopy Perturbation Method for nonlinear differential-difference equations. Int. J. Comput. Math. (2008) 10.1080/00207160802247646
    • (2008) Int. J. Comput. Math.
    • Yildirim, A.1
  • 20
    • 58449094572 scopus 로고    scopus 로고
    • The homotopy perturbation method for approximate solution of the modified KdV equation
    • Yi{dotless}ldi{dotless}ri{dotless}m A. The homotopy perturbation method for approximate solution of the modified KdV equation. Z. Naturforsch. 63a (2008) 621-626
    • (2008) Z. Naturforsch. , vol.63 a , pp. 621-626
    • Yildirim, A.1
  • 21
    • 50949124409 scopus 로고    scopus 로고
    • Recent development of the homotopy perturbation method
    • He J.H. Recent development of the homotopy perturbation method. Topol. Methods. Non linear Anal. 31 (2008) 205-209
    • (2008) Topol. Methods. Non linear Anal. , vol.31 , pp. 205-209
    • He, J.H.1
  • 22
    • 58149216130 scopus 로고    scopus 로고
    • An elementary introduction to the homotopy perturbation method
    • He J.H. An elementary introduction to the homotopy perturbation method. Comput. Math. Appl. 57 (2009) 410-412
    • (2009) Comput. Math. Appl. , vol.57 , pp. 410-412
    • He, J.H.1
  • 23
    • 0000615571 scopus 로고
    • An approximate solution technique not depending on small parameters: A special example
    • 371-180
    • Liao S.J. An approximate solution technique not depending on small parameters: A special example. Int. J. Non linear Mech. 36 (1995) 371-180
    • (1995) Int. J. Non linear Mech. , vol.36
    • Liao, S.J.1
  • 25
    • 64449088045 scopus 로고    scopus 로고
    • Convergence of the homotopy perturbation method for partial differential equations
    • 10.1016/j.nonrwa.2008.07.002
    • Biazar J., and Ghazvini H. Convergence of the homotopy perturbation method for partial differential equations. Non Linear Anal. RWA (2008) 10.1016/j.nonrwa.2008.07.002
    • (2008) Non Linear Anal. RWA
    • Biazar, J.1    Ghazvini, H.2
  • 26
    • 38049015848 scopus 로고    scopus 로고
    • The homotopy analysis method for Cauchy reaction-diffusion problems
    • Sami Bataineh A., Noorani M.S.M., and Hashim I. The homotopy analysis method for Cauchy reaction-diffusion problems. Phys. Lett. A 372 5 (2008) 613-618
    • (2008) Phys. Lett. A , vol.372 , Issue.5 , pp. 613-618
    • Sami Bataineh, A.1    Noorani, M.S.M.2    Hashim, I.3
  • 27
    • 35348973440 scopus 로고    scopus 로고
    • Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method
    • Sami Bataineh A., Noorani M.S.M., and Hashim I. Solutions of time-dependent Emden-Fowler type equations by homotopy analysis method. Phys. Lett. A 371 (2007) 72-82
    • (2007) Phys. Lett. A , vol.371 , pp. 72-82
    • Sami Bataineh, A.1    Noorani, M.S.M.2    Hashim, I.3
  • 28
    • 34548249064 scopus 로고    scopus 로고
    • Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method
    • Yi{dotless}ldi{dotless}ri{dotless}m A., and Öziş T. Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method. Phys. Lett. A 369 (2007) 70-76
    • (2007) Phys. Lett. A , vol.369 , pp. 70-76
    • Yildirim, A.1    Öziş, T.2
  • 29
    • 34248375297 scopus 로고    scopus 로고
    • A new modification of the homotopy perturbation method for linear and nonlinear operators
    • Odibat Z. A new modification of the homotopy perturbation method for linear and nonlinear operators. Appl. Math. Comput. 189 (2007) 746-753
    • (2007) Appl. Math. Comput. , vol.189 , pp. 746-753
    • Odibat, Z.1


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