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Volumn 9, Issue 4, 2008, Pages 395-408

Homotopy perturbation method for solving nonlinear higher-order boundary value problems

Author keywords

Boussinesq equations; Error estimates; Homotopy perturbation method; Nonlinear boundary value problems; Thomas Fermi equation

Indexed keywords


EID: 51749118465     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2008.9.4.395     Document Type: Article
Times cited : (55)

References (62)
  • 1
    • 34249032106 scopus 로고    scopus 로고
    • S. Abbasbandy, Numerical solutions of nonlinear Klein-Cordon equation by variational iteration method, Internat. J. Numer. Mech. Engg. 70 (2007), 876-881.
    • S. Abbasbandy, Numerical solutions of nonlinear Klein-Cordon equation by variational iteration method, Internat. J. Numer. Mech. Engg. 70 (2007), 876-881.
  • 2
    • 34250615490 scopus 로고    scopus 로고
    • A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials
    • S. Abbasbandy, A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials, J. Comput. Appl. Math. 207 (2007), 59-63.
    • (2007) J. Comput. Appl. Math , vol.207 , pp. 59-63
    • Abbasbandy, S.1
  • 3
    • 27144467065 scopus 로고    scopus 로고
    • New applications of variational iteration method
    • M. A. Abdou and A. A. Soliman, New applications of variational iteration method, Phys. D 211 (1-2) (2005), 1-8.
    • (2005) Phys. D , vol.211 , Issue.1-2 , pp. 1-8
    • Abdou, M.A.1    Soliman, A.A.2
  • 4
    • 41949112904 scopus 로고    scopus 로고
    • O. Abdulaziz, I. Hashim and S. Momani, Application of homotopy perturbation method to fractional IVPs, J. Comput. Appl. Math. (2007), doi: 10.1016/j.cam.2007.06.010.
    • O. Abdulaziz, I. Hashim and S. Momani, Application of homotopy perturbation method to fractional IVPs, J. Comput. Appl. Math. (2007), doi: 10.1016/j.cam.2007.06.010.
  • 5
    • 37549050173 scopus 로고    scopus 로고
    • O. Abdulaziz, I. Hashim and S. Momani, Solving systems of fractional differential equations by homotopy perturbation method, Phys. Let. A (2007), doi:10.1016/j.physleta.2007.07.059.2.
    • O. Abdulaziz, I. Hashim and S. Momani, Solving systems of fractional differential equations by homotopy perturbation method, Phys. Let. A (2007), doi:10.1016/j.physleta.2007.07.059.2.
  • 7
    • 0002634477 scopus 로고
    • Finite-difference methods for the solution of special eighth-order boundary-value problems
    • A. Boutayeb and E. H. Twizell, Finite-difference methods for the solution of special eighth-order boundary-value problems, Int. J. Comput. Math., 48 (1993), 63-75.
    • (1993) Int. J. Comput. Math , vol.48 , pp. 63-75
    • Boutayeb, A.1    Twizell, E.H.2
  • 8
    • 0002061853 scopus 로고
    • Numerical methods for the solution of special sixth-order boundary value problems
    • A. Boutayeb and E. H. Twizell, Numerical methods for the solution of special sixth-order boundary value problems, Int. J. Comput. Math 45 (1992), 207-233.
    • (1992) Int. J. Comput. Math , vol.45 , pp. 207-233
    • Boutayeb, A.1    Twizell, E.H.2
  • 9
    • 0024681691 scopus 로고    scopus 로고
    • R. E. D. Bishop, S. M. Cannon and S. Miao, On coupled bending and torsional vibration of uniform beams, J. Sod. Vibn. 131 (1989), 457-464.
    • R. E. D. Bishop, S. M. Cannon and S. Miao, On coupled bending and torsional vibration of uniform beams, J. Sod. Vibn. 131 (1989), 457-464.
  • 11
    • 65449158498 scopus 로고    scopus 로고
    • The multistage homotopy perturbation method: A powerful scheme for handling the Lorenz system
    • doi:10.1016/j.chaos.2007.09.073
    • M. S. Chowdhury, I. Hashim and S. Momani, The multistage homotopy perturbation method: A powerful scheme for handling the Lorenz system. Chaos, Solitons & Fractals, (2007), doi:10.1016/j.chaos.2007.09.073.
    • (2007) Chaos, Solitons & Fractals
    • Chowdhury, M.S.1    Hashim, I.2    Momani, S.3
  • 12
    • 38249002885 scopus 로고
    • Numerical methods for special nonlinear boundary-value problems of order 2 m
    • K. Djidjeli, E. H. Twizell and A. Boutayeb, Numerical methods for special nonlinear boundary-value problems of order 2 m, J. Comput. Appl. Math. 47 (1993), 35-45.
    • (1993) J. Comput. Appl. Math , vol.47 , pp. 35-45
    • Djidjeli, K.1    Twizell, E.H.2    Boutayeb, A.3
  • 13
    • 84902861814 scopus 로고
    • Numerical simulations of stellar convection dynamics at the base of the convection zone, geophysics
    • G. A. Glatzmaier, Numerical simulations of stellar convection dynamics at the base of the convection zone, geophysics. Fluid Dynamics 31 (1985), 137-150.
    • (1985) Fluid Dynamics , vol.31 , pp. 137-150
    • Glatzmaier, G.A.1
  • 14
    • 34249865652 scopus 로고    scopus 로고
    • He's homotopy perturbation method for calculating Adomian's polynomials
    • A. Ghorbani and J. S. Nadjfi, He's homotopy perturbation method for calculating Adomian's polynomials, Int. J. Nonlin. Scne. Num. Simul. 8 (2) (2007), 229-332.
    • (2007) Int. J. Nonlin. Scne. Num. Simul , vol.8 , Issue.2 , pp. 229-332
    • Ghorbani, A.1    Nadjfi, J.S.2
  • 15
    • 38849126350 scopus 로고    scopus 로고
    • A. Ghorbani, Beyond Adomian's polynomials: He polynomials, Chas. Soltn. Fract. (2007), doi:10.1016/j.chaos.2007.06.034.
    • A. Ghorbani, Beyond Adomian's polynomials: He polynomials, Chas. Soltn. Fract. (2007), doi:10.1016/j.chaos.2007.06.034.
  • 16
    • 0037844986 scopus 로고    scopus 로고
    • Variational approach to the sixth order boundary value problems
    • J. H. He, Variational approach to the sixth order boundary value problems, Appl. Math. Comput. 143(2003), 235-236.
    • (2003) Appl. Math. Comput , vol.143 , pp. 235-236
    • He, J.H.1
  • 17
    • 34250668369 scopus 로고    scopus 로고
    • Variational iteration method-Some recent results and new interpretations
    • J. H. He, Variational iteration method-Some recent results and new interpretations, J. Comp. Appl. Math. 207 (2007), 3-17.
    • (2007) J. Comp. Appl. Math , vol.207 , pp. 3-17
    • He, J.H.1
  • 18
    • 34748870677 scopus 로고    scopus 로고
    • Variational iteration method: New developments and applications
    • J. H. He and X. Wu, Variational iteration method: New developments and applications, Comput. Math. Appl. 54(2007), 881-894.
    • (2007) Comput. Math. Appl , vol.54 , pp. 881-894
    • He, J.H.1    Wu, X.2
  • 19
    • 0000092673 scopus 로고    scopus 로고
    • Variational iteration method, A kind of non-linear analytical technique, some examples
    • J. H. He, Variational iteration method, A kind of non-linear analytical technique, some examples, Internat. J. Nonlinear Mech. 34 (4) (1999), 699-708.
    • (1999) Internat. J. Nonlinear Mech , vol.34 , Issue.4 , pp. 699-708
    • He, J.H.1
  • 20
    • 0040184009 scopus 로고    scopus 로고
    • Variational iteration method for autonomous ordinary differential systems
    • J. H. He, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput. 114 (2-3) (2000), 115-123.
    • (2000) Appl. Math. Comput , vol.114 , Issue.2-3 , pp. 115-123
    • He, J.H.1
  • 21
    • 85126452772 scopus 로고    scopus 로고
    • J. H. He and X. H. Wu, Construction of solitary solution and compaction-like solution by Variational iteration method, Chas. Solton. Fract. 29 (1) (2006), 108-113.
    • J. H. He and X. H. Wu, Construction of solitary solution and compaction-like solution by Variational iteration method, Chas. Solton. Fract. 29 (1) (2006), 108-113.
  • 22
    • 36148932234 scopus 로고    scopus 로고
    • The variational iteration method for eighth-order initial boundary value problems
    • J. H. He, The variational iteration method for eighth-order initial boundary value problems, Phys. Scr. 76(6) (2007), 680-682.
    • (2007) Phys. Scr , vol.76 , Issue.6 , pp. 680-682
    • He, J.H.1
  • 23
    • 33645972898 scopus 로고    scopus 로고
    • J. H. He, Some asymptotic methods for strongly nonlinear equation, Int. J. Mod. Phys. 20 (20)10 (2006), 1144-1199.
    • J. H. He, Some asymptotic methods for strongly nonlinear equation, Int. J. Mod. Phys. 20 (20)10 (2006), 1144-1199.
  • 24
    • 0032672778 scopus 로고    scopus 로고
    • J. H. He, Homotopy perturbation technique, Comput. Math. Appl. Mech, Engy. (1999), 178-257.
    • J. H. He, Homotopy perturbation technique, Comput. Math. Appl. Mech, Engy. (1999), 178-257.
  • 25
    • 30644460357 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving boundary value problems
    • J. H. He, 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
  • 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, Appl. Math. Comput. 156 (2004), 527-539.
    • (2004) Appl. Math. Comput , vol.156 , pp. 527-539
    • He, J.H.1
  • 27
    • 17844387391 scopus 로고    scopus 로고
    • Homotopy perturbation method for bifurcation of nonlinear problems
    • J. H. He, Homotopy perturbation method for bifurcation of nonlinear problems, Int. J. Nonlin. Sci Numer. Simul. 6 (2) (2005), 207-208.
    • (2005) Int. J. Nonlin. Sci Numer. Simul , vol.6 , Issue.2 , pp. 207-208
    • He, J.H.1
  • 28
    • 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, Appl. Math. Comput. 151 (2004), 287-292.
    • (2004) Appl. Math. Comput , vol.151 , pp. 287-292
    • He, J.H.1
  • 29
    • 0033702384 scopus 로고    scopus 로고
    • A coupling method of homotopy technique and perturbation technique for nonlinear problems
    • J. H. He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Nonlin. Mech. 35 (1) (2000), 115-123.
    • (2000) Int. J. Nonlin. Mech , vol.35 , Issue.1 , pp. 115-123
    • He, J.H.1
  • 30
    • 33745177020 scopus 로고    scopus 로고
    • Exp-function method for nonlinear wave equations
    • J. H. He and X. H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons. Fract. 30 (3) (2006), 700-708.
    • (2006) Chaos Solitons. Fract , vol.30 , Issue.3 , pp. 700-708
    • He, J.H.1    Wu, X.H.2
  • 31
    • 34250163508 scopus 로고    scopus 로고
    • New periodic solutions for nonlinear evolution equation using Exp-method, Chaos Solitons
    • J. H. He and M. A. Abdou, New periodic solutions for nonlinear evolution equation using Exp-method, Chaos Solitons. Farct.34 (2007), 1421-1429.
    • (2007) Farct , vol.34 , pp. 1421-1429
    • He, J.H.1    Abdou, M.A.2
  • 32
    • 0006996396 scopus 로고
    • General use of the Lagrange multiplier in nonlinear mathematical physics
    • S. Nemat-Naseer Ed, Pergamon press, New York
    • M. Inokuti, H. Sekine and T. Mura, General use of the Lagrange multiplier in nonlinear mathematical physics, in: S. Nemat-Naseer (Ed.), Variational method in the Mechanics of solids, Pergamon press, New York, (1978), 156-162.
    • (1978) Variational method in the Mechanics of solids , pp. 156-162
    • Inokuti, M.1    Sekine, H.2    Mura, T.3
  • 33
    • 85126476724 scopus 로고    scopus 로고
    • S. Momani and Z. Odibat, Application of He's variational iteration method to Helmholtz equations, Chas. Soltns. Fract. 27 (5) (2006), 1119-1123.
    • S. Momani and Z. Odibat, Application of He's variational iteration method to Helmholtz equations, Chas. Soltns. Fract. 27 (5) (2006), 1119-1123.
  • 34
    • 34247395044 scopus 로고    scopus 로고
    • homotopy perturbation method for nonlinear partial differential equations of fractional order
    • S. Momani and Z. Odibat, homotopy perturbation method for nonlinear partial differential equations of fractional order, Phys. Let. A 365, (2007) 345-350.
    • (2007) Phys. Let. A , vol.365 , pp. 345-350
    • Momani, S.1    Odibat, Z.2
  • 35
    • 34748865972 scopus 로고    scopus 로고
    • Comparison between homotopy perturbation method and variational iteration method for linear fractional partial differential equations
    • S. Momani and Z. Odibat, Comparison between homotopy perturbation method and variational iteration method for linear fractional partial differential equations, Comput. Math. Appl. 54 (2007), 910-919.
    • (2007) Comput. Math. Appl , vol.54 , pp. 910-919
    • Momani, S.1    Odibat, Z.2
  • 37
    • 33846688136 scopus 로고    scopus 로고
    • S. T. Mohyud-Din and M. A Noor, Homotopy perturbation method for solving fourth order boundary value problems, Math. Prob. Engg. (2007), 1-15, Article ID 98602, doi:10.1155/2007/98602.
    • S. T. Mohyud-Din and M. A Noor, Homotopy perturbation method for solving fourth order boundary value problems, Math. Prob. Engg. (2007), 1-15, Article ID 98602, doi:10.1155/2007/98602.
  • 38
    • 33845572723 scopus 로고    scopus 로고
    • An efficient algorithm for solving fifth order boundary value problems
    • M. A. Noor and S.T. Mohyud-Din, An efficient algorithm for solving fifth order boundary value problems, Math. Comput. Modl. 45 (2007), 954-964.
    • (2007) Math. Comput. Modl , vol.45 , pp. 954-964
    • Noor, M.A.1    Mohyud-Din, S.T.2
  • 39
    • 42749094344 scopus 로고    scopus 로고
    • Homotopy perturbation method for solving sixth-order boundary value problems
    • M. A. Noor and S. T. Mohyud-Din, Homotopy perturbation method for solving sixth-order boundary value problems, Comput. Math. Appl. 55 (12) (2008), 2953-2972.
    • (2008) Comput. Math. Appl , vol.55 , Issue.12 , pp. 2953-2972
    • Noor, M.A.1    Mohyud-Din, S.T.2
  • 40
    • 42749097785 scopus 로고    scopus 로고
    • Homotopy method for solving eighth order boundary value problem
    • M. A. Noor and S. T. Mohyud-Din, Homotopy method for solving eighth order boundary value problem, J. Math. Anal. Appl. Th. 1(2) (2006), 161-169.
    • (2006) J. Math. Anal. Appl. Th , vol.1 , Issue.2 , pp. 161-169
    • Noor, M.A.1    Mohyud-Din, S.T.2
  • 41
    • 43949130316 scopus 로고    scopus 로고
    • Approximate solutions of Flieral Petviashivili equation and its variants
    • M. A. Noor and S. T. Mohyud-Din, Approximate solutions of Flieral Petviashivili equation and its variants, Int. J. Math. Comput. Scne. 2 (4) (2007), 345-360.
    • (2007) Int. J. Math. Comput. Scne , vol.2 , Issue.4 , pp. 345-360
    • Noor, M.A.1    Mohyud-Din, S.T.2
  • 42
    • 47649100260 scopus 로고    scopus 로고
    • A reliable approach for solving linear and nonlinear sixth-order boundary value problems
    • M. A. Noor and S. T. Mohyud-Din, A reliable approach for solving linear and nonlinear sixth-order boundary value problems, Int. J. Comput. Appl. Math. 2 (2) (2007), 163-172.
    • (2007) Int. J. Comput. Appl. Math , vol.2 , Issue.2 , pp. 163-172
    • Noor, M.A.1    Mohyud-Din, S.T.2
  • 44
    • 43749107936 scopus 로고    scopus 로고
    • Variational iteration method for solving higher-order nonlinear boundary value problems using He's polynomials
    • M. A. Noor and S. T. Mohyud-Din, Variational iteration method for solving higher-order nonlinear boundary value problems using He's polynomials, Int. J. Nonlin. Scne. Num. Simul. 9 (2) (2008).
    • (2008) Int. J. Nonlin. Scne. Num. Simul , vol.9 , Issue.2
    • Noor, M.A.1    Mohyud-Din, S.T.2
  • 45
    • 43949104375 scopus 로고    scopus 로고
    • M. A. Noor and S. T. Mohyud-Din, Variational iteration method for solving fifth-order boundary value problems using He's polynomials, Math. Prob. Engg. (2008), Article ID 954794, doi: 10:1155/2008/954794.
    • M. A. Noor and S. T. Mohyud-Din, Variational iteration method for solving fifth-order boundary value problems using He's polynomials, Math. Prob. Engg. (2008), Article ID 954794, doi: 10:1155/2008/954794.
  • 46
    • 34249046099 scopus 로고    scopus 로고
    • Variational iteration technique for solving higher order boundary value problems
    • M. A. Noor and S. T. Mohyud-Din, Variational iteration technique for solving higher order boundary value problems, Appl. Math. Comput. 189 (2007), 1929-1942.
    • (2007) Appl. Math. Comput , vol.189 , pp. 1929-1942
    • Noor, M.A.1    Mohyud-Din, S.T.2
  • 47
    • 34748891700 scopus 로고    scopus 로고
    • An efficient method for fourth order boundary value problems
    • M. A. Noor and S. T. Mohyud-Din, An efficient method for fourth order boundary value problems, Comput. Math. Appl. 54 (2007), 1101-1111.
    • (2007) Comput. Math. Appl , vol.54 , pp. 1101-1111
    • Noor, M.A.1    Mohyud-Din, S.T.2
  • 50
    • 52949152408 scopus 로고    scopus 로고
    • Exp-function method for generalized travelling solutions of master partial differential equations, Acta Applnda
    • DOI: 10.1007/s10440-008-9245-z
    • M. A. Noor, S. T. Mohyud-Din and A. Waheed, Exp-function method for generalized travelling solutions of master partial differential equations, Acta Applnda. Mathmtce. (2008), DOI: 10.1007/s10440-008-9245-z.
    • (2008) Mathmtce
    • Noor, M.A.1    Mohyud-Din, S.T.2    Waheed, A.3
  • 51
    • 85121076638 scopus 로고    scopus 로고
    • M. A. Noor, S. T. Mohyud-Din and A. Waheed, Exp-function method for solving Kuramoto-Sivashinsky and Boussinesq equations, J. Appl. Math. Computg. (2008), DOI: 10.1007/s12190-008-0083-y.
    • M. A. Noor, S. T. Mohyud-Din and A. Waheed, Exp-function method for solving Kuramoto-Sivashinsky and Boussinesq equations, J. Appl. Math. Computg. (2008), DOI: 10.1007/s12190-008-0083-y.
  • 53
    • 35348869861 scopus 로고    scopus 로고
    • Modified homotopy perturbation method: Application to quadratic Riccati differential equations of fractional order
    • Z. Odibat and S. Momani, Modified homotopy perturbation method: application to quadratic Riccati differential equations of fractional order, Chas. Soltn. Frctl. 36 (2008), 167-174.
    • (2008) Chas. Soltn. Frctl , vol.36 , pp. 167-174
    • Odibat, Z.1    Momani, S.2
  • 54
    • 47049110747 scopus 로고    scopus 로고
    • On the variational iteration method and other iterative techniques for nonlinear differential equations
    • in press
    • J. I. Ramos, On the variational iteration method and other iterative techniques for nonlinear differential equations, Appl. Math. Comput. (2007), in press.
    • (2007) Appl. Math. Comput
    • Ramos, J.I.1
  • 55
    • 0030149129 scopus 로고    scopus 로고
    • Spline solution of linear eighth-order boundary value problems
    • S. S. Siddiqi and E. H. Twizell, Spline solution of linear eighth-order boundary value problems, Comput. Math. Appl. Mech. Engg. 131 (1996), 309-325.
    • (1996) Comput. Math. Appl. Mech. Engg , vol.131 , pp. 309-325
    • Siddiqi, S.S.1    Twizell, E.H.2
  • 56
    • 0034276401 scopus 로고    scopus 로고
    • Approximate solutions to boundary value problems of higher-order by the modified decomposition method
    • A. M. Wazwaz, Approximate solutions to boundary value problems of higher-order by the modified decomposition method, Comput. Math. Appl. 40(2000), 679-691.
    • (2000) Comput. Math. Appl , vol.40 , pp. 679-691
    • Wazwaz, A.M.1
  • 57
    • 0005248526 scopus 로고    scopus 로고
    • The modified decomposition method for solving linear and nonlinear boundary value problems of tenth-order and twelfth-order
    • A. M. Wazwaz, The modified decomposition method for solving linear and nonlinear boundary value problems of tenth-order and twelfth-order, Int. J. Nonlin. Scne. Num. Simul. 1 (2000), 17-24.
    • (2000) Int. J. Nonlin. Scne. Num. Simul , vol.1 , pp. 17-24
    • Wazwaz, A.M.1
  • 58
    • 43949100518 scopus 로고    scopus 로고
    • The numerical solutions of special eighth-order boundary value problems by the modified decomposition method
    • A. M. Wazwaz, The numerical solutions of special eighth-order boundary value problems by the modified decomposition method, Neu. Parll. Sci. Comput. 8(2) (2000), 133-146.
    • (2000) Neu. Parll. Sci. Comput , vol.8 , Issue.2 , pp. 133-146
    • Wazwaz, A.M.1
  • 59
    • 0035281487 scopus 로고    scopus 로고
    • The numerical solution of sixth order boundary value problems by the modified decomposition method
    • A. M. Wazwaz, The numerical solution of sixth order boundary value problems by the modified decomposition method, Appl. Math. Comput. 118 (2001), 311-325.
    • (2001) Appl. Math. Comput , vol.118 , pp. 311-325
    • Wazwaz, A.M.1
  • 60
    • 0002751751 scopus 로고    scopus 로고
    • The modified decomposition method and Fade approximants for solving Thomas-Fermi equation
    • A. M. Wazwaz, The modified decomposition method and Fade approximants for solving Thomas-Fermi equation, Appl. Math. Comput. 105 (1999), 11-19.
    • (1999) Appl. Math. Comput , vol.105 , pp. 11-19
    • Wazwaz, A.M.1
  • 61
    • 43049172565 scopus 로고    scopus 로고
    • The variational iteration method for fourth-order boundary value problems
    • in press
    • L. Xu, The variational iteration method for fourth-order boundary value problems, Chas. Solton. Fract. (2007), in press.
    • (2007) Chas. Solton. Fract
    • Xu, L.1
  • 62
    • 34748871953 scopus 로고    scopus 로고
    • He's homotopy perturbation method for a boundary layer equation in unbounded domain
    • L. Xu, He's homotopy perturbation method for a boundary layer equation in unbounded domain, Comput. Math. Appl. 54 (2007), 1067-1070.
    • (2007) Comput. Math. Appl , vol.54 , pp. 1067-1070
    • Xu, L.1


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