×

zbMATH — the first resource for mathematics

Asymptotology by homotopy perturbation method. (English) Zbl 1061.65040
Summary: An heuristical example is given to illustrate the basic idea of the homotopy perturbation method, so that homotopy perturbation method has made all that is necessary simple, and all that is complex unnecessary.

MSC:
65H05 Numerical computation of solutions to single equations
65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Andrianov, I.; Awrejcewicz, J., Construction of periodic solution to partial differential equations with nonlinear boundary conditions, International journal of nonlinear sciences and numerical simulation, 1, 4, 327-332, (2000) · Zbl 0977.35031
[2] Andrianov, I.; Manevitch, L., Asymptotology: ideas, methods, and applications, (2003), Kluwer Academic Publishers
[3] Bender, C.M.; Pinsky, K.S.; Simmons, L.M., A new perturbative approach to nonlinear problems, Journal of mathematical physics, 30, 7, 1447-1455, (1989) · Zbl 0684.34008
[4] Delamotte, B., Nonperturbative method for solving differential equations and finding limit cycles, Physical review letters, 70, 3361-3364, (1993) · Zbl 1051.65505
[5] He, J.H., Variational iteration method: a kind of nonlinear analytical technique: some examples, International journal of nonlinear mechanics, 34, 4, 699-708, (1999) · Zbl 1342.34005
[6] He, J.H., Homotopy perturbation technique, Computer methods in applied mechanics and engineering, 178, 257-262, (1999) · Zbl 0956.70017
[7] He, J.H., A coupling method of homotopy technique and perturbation technique for nonlinear problems, International journal of nonlinear mechanics, 35, 1, 37-43, (2000) · Zbl 1068.74618
[8] He, J.H., A review on some new recently developed nonlinear analytical techniques, International journal of nonlinear sciences and numerical simulation, 1, 1, 51-70, (2000) · Zbl 0966.65056
[9] He, J.H., Bookkeeping parameter in perturbation methods, International journal of nonlinear science and numerical simulation, 2, 3, 257-264, (2001) · Zbl 1072.34508
[10] He, J.H., Modified lindstedt – poincare methods for some strongly nonlinear oscillations. part III: double series expansion, International journal of nonlinear science and numerical simulation, 2, 4, 317-320, (2001) · Zbl 1072.34507
[11] He, J.H., Iteration perturbation method for strongly nonlinear oscillations, Journal of vibration and control, 7, 5, 631-642, (2001) · Zbl 1015.70019
[12] He, J.H., A note on delta-perturbation expansion method, Applied mathematics and mechanics, 23, 6, 634-638, (2002) · Zbl 1029.34043
[13] He, J.H., Recent developments in asymptotic methods for nonlinear ordinary equations, Invited lecture delivered at 10th international colloquium on numerical analysis and computer science with applications, Plovidiv, Bulgaria, 12-17 August 2001, International journal of computational and numerical analysis and applications, 2, 2, 127-190, (2002) · Zbl 1046.34001
[14] He, J.H., Homotopy perturbation method: a new nonlinear analytical technique, Applied mathematics and computation, 135, 73-79, (2003) · Zbl 1030.34013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.