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Öziş, Turgut; Yıldırım, Ahmet

Comparison between Adomian’s method and He’s homotopy perturbation method. (English) Zbl 1155.65344

Comput. Math. Appl. 56, No. 5, 1216-1224 (2008).
Summary: In this paper, it is revealed that modified form of He’s homotopy perturbation method corresponds to Adomian’s decomposition method for certain nonlinear problems.

Cited in 26 Documents

MSC:

65J15 Numerical solutions to equations with nonlinear operators

Keywords:

He’s homotopy perturbation method; Adomian’s decomposition method; Taylor expansion; nonlinear problems; Bratu-type problems
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\textit{T. Öziş} and \textit{A. Yıldırım}, Comput. Math. Appl. 56, No. 5, 1216--1224 (2008; Zbl 1155.65344)
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References:

[1] He, J.H., Homotopy perturbation technique, Computer methods in applied mechanics and engineering, 178, 3-4, 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, International journal of non-linear mechanics, 35, 1, 37-43, (2000) · Zbl 1068.74618
[3] He, J.H., Homotopy perturbation method: A new nonlinear analytical technique, Applied mathematics and computation, 135, 1, 73-79, (2003) · Zbl 1030.34013
[4] He, J.H., New interpretation of homotopy perturbation method, International journal of modern physics B, 20, 18, 2561-2568, (2006)
[5] He, J.H., Homotopy perturbation method for solving boundary value problems, Physics letters A, 350, 1-2, 87-88, (2006) · Zbl 1195.65207
[6] J.H. He, Non-Perturbative Methods for Strongly Nonlinear Problems, dissertation. de-verlag im Internet GmbH, Berlin, 2006
[7] Öziş, T.; Yıldırım, A., A note on he’s homotopy perturbation method for van der Pol oscillator with very strong nonlinearity, Chaos solitons & fractals, 37, 989-991, (2007)
[8] Öziş, T.; Yıldırım, A., Traveling wave solution of Korteweg-de Vries equation using he’s homotopy perturbation method, International journal of nonlinear sciences and numerical simulation, 8, 2, 239-242, (2007)
[9] Öziş, T.; Yıldırım, A., A comparative study of he’s homotopy perturbation method for determining frequency – amplitude relation of a non-linear oscillator with discontinuities, International journal of nonlinear sciences and numerical simulation, 8, 2, 243-248, (2007)
[10] Yıldırım, A.; Öziş, T., Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method, Physics letters A, 369, 70-76, (2007) · Zbl 1209.65120
[11] Dehghan, M.; Shakeri, F., Solution of an integro-differential equation arising in oscillating magnetic fields using he’s homotopy perturbation method, Progress in electromagmentics research, PIER, 78, 361-376, (2008)
[12] Shakeri, F.; Dehghan, M., Inverse problem of diffusion equation by he’s homotopy perturbation method, Physica scripta, 75, 551-556, (2007) · Zbl 1110.35354
[13] Dehghan, M.; Shakeri, F., Solution of a partial differential equation subject to temperature overspecification by he’s homotopy perturbation method, Physica scripta, 75, 778-787, (2007) · Zbl 1117.35326
[14] Shakeri, F.; Dehghan, M., Solution of delay differential equations via a homotopy perturbation method, Mathematical and computer modelling, (2007)
[15] Adomian, G., A review of the decomposition method and some recent results for nonlinear equation, Mathematical and computer modelling, 13, 7, 17-43, (1992) · Zbl 0713.65051
[16] Adomian, G., A review of the decomposition method in applied mathematics, Journal of mathematical analysis and application, 135, 501-544, (1988) · Zbl 0671.34053
[17] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer Dordrecht · Zbl 0802.65122
[18] Wazwaz, A.-M., A reliable modification of adomian’s decomposition method, Applied mathematics and computation, 92, 1-7, (1998)
[19] Wazwaz, A.-M., A comparison between Adomian decomposition method and Taylor series method in the series solution, Applied mathematics and computation, 79, 37-44, (1998) · Zbl 0943.65084
[20] Wazwaz, A.-M., Adomian decomposition method for a reliable treatment of the bratu-type equations, Applied mathematics and computation, 166, 652-663, (2005) · Zbl 1073.65068
[21] Wazwaz, A.-M., Partial differential equations: methods and applications, (2002), Balkema Publishers The Netherlands
[22] Wazwaz, A.-M., A new algorithm for calculating Adomian polynomials for nonlinear operators, Applied mathematics and computation, 111, 53-69, (2000) · Zbl 1023.65108
[23] Deeba, E.; Khuri, S.A.; Xie, S., An algorithm for solving boundary value problems, Journal of computational physics, 159, 125-138, (2000) · Zbl 0959.65091
[24] Biazar, J.; Babolian, E.; Kember, G.; Nouri, A.; Islam, R., An alternative algorithm for computing Adomian polynomials in special cases, Applied mathematics and computation, 138, 523-529, (2003) · Zbl 1027.65076
[25] Babolian, E.; Javadi, Sh., New method for calculating Adomian polynomials, Applied mathematics and computation, 153, 253-259, (2004) · Zbl 1055.65068
[26] Zhu, Y.; Chang, Q.; Wu, S., A new algorithm for calculating Adomian polynomials, Applied mathematics and computation, 169, 402-416, (2005) · Zbl 1087.65528
[27] Pourdarvish, A., A reliable symbolic implementation of algorithm for calculating Adomian polynomials, Applied mathematics and computation, 172, 545-550, (2006) · Zbl 1088.65021
[28] Ghorbani, A.; Saber-Nadjafi, J., He’s homotopy perturbation method for calculating Adomian polynomials, International journal of nonlinear sciences and numerical simulation, 8, 2, 229-232, (2007) · Zbl 1401.65056
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