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Abdou, M. A.; Soliman, A. A.

Variational iteration method for solving Burgers and coupled Burgers equations. (English) Zbl 1072.65127

J. Comput. Appl. Math. 181, No. 2, 245-251 (2005).
Summary: By means of variational iteration method the solutions of Burgers equation and coupled Burgers equations are exactly obtained, a comparison with the Adomian decomposition method is made, showing that the former is more effective than the later. In this paper, J. H. He’s variational iteration method [Appl. Math. Comput. 114, No. 2–3, 115–123 (2000; Zbl 1027.34009)] is introduced to overcome the difficulty arising in calculating Adomian polynomials.

Cited in 198 Documents

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)

Keywords:

Burger’s equations; Variational iteration method; Lagrange multiplier; comparison of methods; numerical examples; Adomian decomposition method

Citations:

Zbl 1027.34009
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\textit{M. A. Abdou} and \textit{A. A. Soliman}, J. Comput. Appl. Math. 181, No. 2, 245--251 (2005; Zbl 1072.65127)
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References:

[1] Ablowitz, M.J.; Clarkson, P.A., Solitons, nonlinear evolution equations and inverse scattering, (1991), Cambridge University Press Cambridge · Zbl 0762.35001
[2] Adomian, G., Math. comput. modelling, 22, 103, (1995)
[3] Ali, A.H.A.; Gardner, G.A.; Gardner, L.R.T., Comput. methods appl. mech. eng., 100, 325-337, (1992)
[4] Burgers, J., (), 171-199
[5] J. Caldwell, E. Hinton, et al. (Eds.), Numerical Methods for Nonlinear Problems, Pineridge, Swansea, vol. 3, 1987, pp. 253-261.
[6] Caldwell, J.; Wanless, P.; Cook, A.E., Appl. math. modelling, 5, 189-193, (1981)
[7] A. Coely, et al. (Eds.), Backlund and Darboux Transformations, American Mathematical Society, Providence, RI, 2001.
[8] Cole, J.D., Quart. appl. math., 9, 225-236, (1951)
[9] Draganescu, Gh.E.; Capalnasan, V., Internat. J. nonlinear sci. numer. simulation, 4, 219-226, (2004)
[10] Esipov, S.E., Phys. rev. E, 52, 3711-3718, (1995)
[11] Fan, E., Phys. lett. A, 282, 18, (2001)
[12] Fan, E.G.; Zhang, H.Q., Phys. lett. A, 246, 403, (1998)
[13] Gardner, C.S.; Green, J.M.; Kruskal, M.D.; Miura, R.M., Phys. rev. lett., 19, 1095, (1967)
[14] He, J.H., Comm. nonlinear sci. numer. simulation, 2, 4, 230-235, (1997)
[15] He, J.H., Comput. methods appl. mech. eng., 167, 57-68, (1998)
[16] He, J.H., Comput. methods appl. mech. eng., 167, 69-73, (1998)
[17] He, J.H., Internat. J. non-linear mech., 34, 699-708, (1999) · Zbl 1342.34005
[18] He, J.H., Appl. math. comput., 114, 2,3, 115-123, (2000)
[19] He, J.H., Approximate analytical methods in science and engineering, (2002), Henan Sci. & Tech. Press Zhengzhou, (in Chinese)
[20] He, J.H., Generalized variational principles in fluids, (2003), Science & Culture Publishing House of China Hong Kong, (in Chinese) · Zbl 1054.76001
[21] Herbst, B.M.; Schoombie, S.W.; Mitchell, A.R., Internat. J. numer. methods eng., 18, 1321-1336, (1982)
[22] Hirota, R., Phys. rev. lett., 27, 1192, (1971)
[23] Hirota, R.; Satsuma, J., Phys. lett. A, 85, 407, (1981)
[24] Hopf, E., The partial differential equation, Comm. pure appl. math., 3, 201-230, (1950) · Zbl 0039.10403
[25] Kaya, D., Internat. J. math. math. sci., 27, 675, (2001)
[26] Kaya, D., Appl. math. comput., 144, 353-363, (2003)
[27] Malfeit, W., Amer. J. phys., 60, 650, (1992)
[28] Malfliet, W., Amer. J. phys., 60, 650, (1992)
[29] Marinca, V., Internat. J. nonlinear sci. numer. simulation, 3, 107-120, (2002)
[30] Nee, J.; Duan, J., Appl. math. lett., 11, 1, 57-61, (1998)
[31] S.G. Rubin, R.A. Graves, Computers and Fluids, vol. 3, Pergamon Press, Oxford, 1975, p. 136.
[32] Satsuma, J.; Hirota, R., J. phys. soc. Japan, 51, 332, (1982)
[33] A.A. Soliman, International Conference on Computational Fluid Dynamics, Beijing, China, October 17-20, 2000, pp. 559-566.
[34] Wadati, M.; Sanuki, H.; Konno, K., Prog. theor. phys., 53, 419, (1975)
[35] Wang, M.L., Phys. lett. A, 215, 279, (1996)
[36] Wazwaz, A.M., Appl. math. comput., 111, 53, (2000)
[37] Wazwaz, A.M., Comput. math. appl., 4, 1237-1244, (2001)
[38] Wazwaz, A.M., Chaos solitons fractical, 12, 2283, (2001)
[39] Wu, Y.T.; Geng, X.G.; Hu, X.B.; Zhu, S.M., Phys. lett. A, 255, 259, (1999)
[40] Yan, C.T., Phys. lett. A, 224, 77, (1996)
[41] Yan, Z.Y.; Zhang, H.Q., Appl. math. mech., 21, 382, (2000)
[42] Yan, Z.Y.; Zhang, H.Q., J. phys. A, 34, 1785, (2001)
[43] Yan, Z.Y.; Zhang, H.Q., Phys. lett. A, 285, 355, (2001)
[44] Yan, Z.Y., Phys. lett. A, 292, 100, (2001)
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