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Homotopy perturbation method: a new nonlinear analytical technique. (English) Zbl 1030.34013

MSC:
34A45Theoretical approximation of solutions of ODE
65L99Numerical methods for ODE
34E99Asymptotic theory of ODE
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Full Text: DOI
References:
[1] G.L. Liu, New research directions in singular perturbation theory: artificial parameter approach and inverse-perturbation technique, in: Conference of 7th Modern Mathematics and Mechanics, Shanghai, 1997
[2] Liao, S. J.: An approximate solution technique not depending on small parameters: a special example. Int. J. Non-linear mech. 30, No. 3, 371-380 (1995) · Zbl 0837.76073
[3] Liao, S. J.: Boundary element method for general nonlinear differential operators. Eng. anal. Boundary elem. 20, No. 2, 91-99 (1997)
[4] He, J. H.: Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. meth. Appl. mech. Eng. 167, 57-68 (1998) · Zbl 0942.76077
[5] He, J. H.: Approximate solution for nonlinear differential equations with convolution product nonlinearities. Comput. meth. Appl. mech. Eng. 167, 69-73 (1998) · Zbl 0932.65143
[6] He, J. H.: Variational iteration method: a kind of nonlinear analytical technique: some examples. Int. J. Non-linear mech. 34, No. 4, 699-708 (1999) · Zbl 05137891
[7] He, J. H.: A review on some new recently developed nonlinear analytical techniques. Int. J. Nonlinear sci. Numer. simul. 1, No. 1, 51-70 (2000) · Zbl 0966.65056
[8] He, J. H.: Homotopy perturbation technique. Comput. meth. Appl. mech. Eng. 178, 257-262 (1999) · Zbl 0956.70017
[9] He, J. H.: A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int. J. Non-linear mech. 35, No. 1, 37-43 (2000) · Zbl 1068.74618
[10] Nayfeh, A. H.: Problems in perturbation. (1985) · Zbl 0573.34001