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.


65J99 Numerical analysis in abstract spaces
Full Text: DOI


[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
[3] He, J. H., Homotopy perturbation method for bifurcation of nonlinear problems, Int J Non-linear Sci Numer Simul, 6, 207-208 (2005) · Zbl 1401.65085
[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
[6] He, J. H., Homotopy perturbation method: a new nonlinear analytical technique, Appl Math Comput, 135, 73-79 (2003) · Zbl 1030.34013
[7] He, J. H., Limit cycle and bifurcation of nonlinear problems, Chaos, Solitons & Fractals, 26, 827-833 (2005) · Zbl 1093.34520
[8] He, J. H., Homotopy perturbation method for solving boundary value problems, Phys Lett A, 350, 87-88 (2006) · Zbl 1195.65207
[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) · Zbl 1119.70017
[11] Cveticanin, L., Homotopy-perturbation method for pure nonlinear differential equation, Chaos, Solitons & Fractals, 30, 1221-1230 (2006) · Zbl 1142.65418
[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) · Zbl 1401.76018
[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
[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) · Zbl 1401.65056
[20] Abassy, T. A.; El-Tawil, M. A.; Saleh, H. K., The solution of Burgers’ and good Boussinesq equations using ADM-Pade technique, Chaos, Solitons & Fractals, 32, 1008-1026 (2007) · Zbl 1130.35111
[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 1401.65087
[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 1401.35010
[23] Adomian, G., Solving frontier problems of physics. The decomposition method (1994), Kluwer: Kluwer Boston, MA · 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
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