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Comments on “R. A. Van Gorder and K. Vajravelu, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 4078–4089”. (English) Zbl 1364.65156
From the text: We divide our comments to [Commun. Nonlinear Sci. Numer. Simul. 14, No. 12, 4078–4089 (2009; Zbl 1221.65208)] into two different parts, one concerns some mistakes in Sections 2 and 3 of the original paper and the other part discusses some conclusions of the mentioned paper.
65L99 Numerical methods for ordinary differential equations
Full Text: DOI
[1] Abbasbandy, S.; Tan, Y.; Liao, S.J., Newton-homotopy analysis method for nonlinear equations, Appl math comput, 188, 1794-1800, (2007) · Zbl 1119.65032
[2] Abbasbandy, S., Application of he’s homotopy perturbation method for Laplace transform, Chaos solitons and fractals, 30, 1206-1212, (2006) · Zbl 1142.65417
[3] Rana, M.A.; Siddiqui, A.M.; Ghori, Q.K.; Qamar, R., Application of he’s homotopy perturbation method to sumudu transform, Int J nonlinear sci numer simul, 8, 185-189, (2008)
[4] Babolian, E.; Saeidian, J.; Paripour, M., Computing the Fourier transform via homotopy perturbation method, Zeitschrift für naturforshung A, 64a, 671-675, (2009)
[5] Liao, S.J., On the relationship between the homotopy analysis method and Euler transform, Commun nonlin sci num simul, 18, 1421-1431, (2010) · Zbl 1221.65206
[6] Liao, S.J., Beyond perturbation: an introduction to homotopy analysis method, (2003), Chapman Hall/CRC Press Boca Raton
[7] Liao, S.J.; Tan, Y., A general approach to obtain series solutions of nonlinear differential equations, Stud appl math, 119, 297355, (2007)
[8] Van Gorder, R.A.; Vajravelu, K., On the selection of auxiliary functions, operators and convergence control parameters in the application of the homotopy analysis method to nonlinear differential equations: A general approach, Commun nonlinear sci numer simul, 14, 4078-4089, (2009) · Zbl 1221.65208
[9] Liao, S.J., Notes on the homotopy analysis method: some definitions and theorems, Commun nonlinear sci numer simul, 14, 983-997, (2009) · Zbl 1221.65126
[10] Liao, S.J., An optimal homotopy-analysis approach for strongly nonlinear differential equations, Commun nonlinear sci num simul, 15, 2003-2016, (2010) · Zbl 1222.65088
[11] Liang, S.X.; Jeffrey, D.J., Comparison of homotopy analysis method and homotopy perturbation method through an evaluation equation, Commun nonlinear sci numer simul, 14, 4057-4064, (2009) · Zbl 1221.65281
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