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Beyond Adomian polynomials: He polynomials. (English) Zbl 1197.65061
Not reviewed. Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

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65J99Numerical analysis in abstract spaces
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References:
[1] He, J. H.: Homotopy perturbation technique, Comput methods appl mech eng 178, 257-262 (1999) · Zbl 0956.70017
[2] He, J. H.: A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Int J non-linear mech 35, 37-43 (2000) · Zbl 1068.74618 · doi:10.1016/S0020-7462(98)00085-7
[3] He, J. H.: Homotopy perturbation method for bifurcation of nonlinear problems, Int J non-linear sci numer simul 6, 207-208 (2005)
[4] He, J. H.: Application of homotopy perturbation method to nonlinear wave equations, Chaos, solitons & fractals 26, 695-700 (2005) · Zbl 1072.35502
[5] He, J. H.: The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl math comput 151, 287-292 (2004) · Zbl 1039.65052 · doi:10.1016/S0096-3003(03)00341-2
[6] He, J. H.: Homotopy perturbation method: a new nonlinear analytical technique, Appl math comput 135, 73-79 (2003) · Zbl 1030.34013 · doi:10.1016/S0096-3003(01)00312-5
[7] He, J. H.: Limit cycle and bifurcation of nonlinear problems, Chaos, solitons & fractals 26, 827-833 (2005) · Zbl 1093.34520 · doi:10.1016/j.chaos.2005.03.007
[8] He, J. H.: Homotopy perturbation method for solving boundary value problems, Phys lett A 350, 87-88 (2006) · Zbl 1195.65207 · doi:10.1016/j.physleta.2005.10.005
[9] Ariel, P. D.; Hayat, T.; Asghar, S.: Homotopy perturbation method and axisymmetric flow over a stretching sheet, Int J non-linear sci numer simul 7, 399-406 (2006)
[10] Beléndez, A.; Hernández, T.; Beléndez: Application of he’s homotopy perturbation method to the Duffing-harmonic oscillator, Int J non-linear sci numer simul 8, 79-88 (2007)
[11] Cveticanin, L.: Homotopy-perturbation method for pure nonlinear differential equation, Chaos, solitons & fractals 30, 1221-1230 (2006) · Zbl 1142.65418 · doi:10.1016/j.chaos.2005.08.180
[12] Ganji, D. D.; Sadighi, A.: Application of he’s homotopy-perturbation method to nonlinear coupled systems of reaction -- diffusion equations, Int J non-linear sci numer simul 7, 411-418 (2006)
[13] Rafei, M.; Ganji, D. D.: Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method, Int J non-linear sci numer simul 7, 321-328 (2006) · Zbl 1160.35517
[14] Siddiqui, A. M.; Mahmood, R.; Ghori, Q. K.: Thin film flow of a third grade fluid on a moving belt by he’s homotopy perturbation method, Int J non-linear sci numer simul 7, 7-14 (2006) · Zbl 1187.76622
[15] Siddiqui, A. M.; Ahmed, M.; Ghori, Q. K.: Couette and Poiseuille flows for non-Newtonian fluids, Int J non-linear sci numer simul 7, 15-26 (2006)
[16] Ozis, T.; Yidirim, A.: Determination of limit cycles by a modified straightforward expansion for nonlinear oscillators, Chaos, solitons & fractals 32, 445-448 (2007)
[17] He, J. H.: Some asymptotic methods for strongly nonlinear equations, Int J mod phys B 20, 1141-1199 (2006) · Zbl 1102.34039 · doi:10.1142/S0217979206033796
[18] He, J. H.: New interpretation of homotopy perturbation method, Int J mod phys B 20, 2561-2568 (2006)
[19] Ghorbani, A.; Saberi-Nadjafi, J.: He’s homotopy perturbation method for calculating Adomian polynomials, Int J non-linear sci numer simul 8, 229-232 (2007)
[20] Abassy, T. A.; El-Tawil, M. A.; Saleh, H. K.: The solution of Burgers and good Boussinesq equations using ADM-Padé technique, Chaos, solitons & fractals 32, 1008-1026 (2007) · Zbl 1130.35111 · doi:10.1016/j.chaos.2005.11.029
[21] Odibat, Z. M.; Momani, S.: Application of variational iteration method to nonlinear differential equations of fractional order, Int J non-linear sci numer simul 7, 27-34 (2006) · Zbl 05675858
[22] Bildik, N.; Konuralp, A.: The use of variational iteration method, differential transform method and Adomian decomposition method for solving different types of nonlinear partial differential equations, Int J non-linear sci numer simul 7, 65-70 (2006) · Zbl 1115.65365
[23] Adomian, G.: Solving frontier problems of physics. The decomposition method, (1994) · Zbl 0802.65122
[24] Adomian, G.: A review of the decomposition method in applied mathematics, J math anal appl 135, 501-544 (1988) · Zbl 0671.34053 · doi:10.1016/0022-247X(88)90170-9