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An elementary introduction to the homotopy perturbation method. (English) Zbl 1165.65374
Summary: This paper is an elementary introduction to the concepts of the homotopy perturbation method. Particular attention is paid to giving an intuitive grasp for the solution procedure throughout the paper.

MSC:
65L99 Numerical methods for ordinary differential equations
65-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis
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[1] Ariel, P.D., The three-dimensional flow past a stretching sheet and the homotopy perturbation method, Comput. math. appl., 54, 920-925, (2007) · Zbl 1138.76029
[2] T.M.A. El-Mistikawy, Comment on the three-dimensional flow past a stretching sheet and the homotopy perturbation method, Comput. Math. Appl., in press (doi:10.1016/j.camwa.2008.06.004)
[3] Ariel, P.D.; Hayat, T.; Asghar, S., Homotopy perturbation method and axisymmetric flow over a stretching sheet, Int. J. nonlinear sci. num., 7, 399-406, (2006)
[4] Belendez, A.; Hernandez, A.; Belendez, T., Application of he’s homotopy perturbation method to the Duffing-harmonic oscillator, Int. J. nonlinear sci. num., 8, 79-88, (2007) · Zbl 1119.70017
[5] Ganji, D.D.; Sadighi, A., Application of he’s homotopy-perturbation method to nonlinear coupled systems of reaction-diffusion equations, Int. J. nonlinear sci. num., 7, 411-418, (2006)
[6] He, J.H., Some asymptotic methods for strongly nonlinear equations, Internat. J. modern phys. B., 20, 1141-1199, (2006) · Zbl 1102.34039
[7] 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. nonlinear sci. num., 7, 7-14, (2006) · Zbl 1187.76622
[8] He, J.H., Modified lindstedt – poincare methods for some strongly nonlinear oscillations part III: double series expansion, Int. J. nonlinear sci. num., 2, 317-320, (2001) · Zbl 1072.34507
[9] He, J.H., Modified lindstedt – poincare methods for some strongly non-linear oscillations part I: expansion of a constant, Internat. J. nonlinear mech., 37, 309-314, (2002) · Zbl 1116.34320
[10] He, J.H., Modified lindstedt – poincare methods for some strongly non-linear oscillations part II: A new transformation, Internat. J. nonlinear mech., 37, 315-320, (2002) · Zbl 1116.34321
[11] He, J.H., Modified straightforward expansion, Meccanica, 34, 287-289, (1999) · Zbl 1002.70019
[12] He, J.H., New interpretation of homotopy perturbation method, Internat. J. modern phys. B, 20, 2561-2568, (2006)
[13] Shou, D.H.; He, J.H., Application of parameter-expanding method to strongly nonlinear oscillators, Int. J. nonlinear sci. num., 8, 121-124, (2007)
[14] Wang, S.Q.; He, J.H., Nonlinear oscillator with discontinuity by parameter-expansion method, Chaos solitons fractals, 35, 688-691, (2008) · Zbl 1210.70023
[15] Xu, L., Application of he’s parameter-expansion method to an oscillation of a mass attached to a stretched elastic wire, Phys. lett. A, 368, 259-262, (2007)
[16] Xu, L., He’s parameter-expanding methods for strongly nonlinear oscillators, J. comput. appl. math., 207, 148-154, (2007) · Zbl 1120.65084
[17] Xu, L., Determination of limit cycle by he’s parameter-expanding method for strongly nonlinear oscillators, J. sound vib., 302, 178-184, (2007) · Zbl 1242.70038
[18] Zhang, L.N.; Xu, L., Determination of the limit cycle by he’s parameter-expansion for oscillators in a \(u(3) /(1 + u(2))\) potential, Z. naturforsch. A, 62, 396-398, (2007) · Zbl 1203.34053
[19] J.H. He, Nonperturbative methods for strongly nonlinear problems, Dissertation.de-Verlag im Internet GmbH 2006
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