El-Wakil, S. A.; Abdou, M. A. New applications of Adomian decomposition method. (English) Zbl 1133.35308 Chaos Solitons Fractals 33, No. 2, 513-522 (2007). Summary: We discuss a new application of Adomian decomposition method on nonlinear physical equations. The models of interest in physics are considered and solved by means of Adomian decomposition method. The behaviour of Adomian solutions and the effects of different values of \(t\) are investigated. Numerical illustrations that include nonlinear physical models are investigated to show the pertinent features of the technique. Cited in 13 Documents MSC: 35A25 Other special methods applied to PDEs 35A35 Theoretical approximation in context of PDEs 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems PDFBibTeX XMLCite \textit{S. A. El-Wakil} and \textit{M. A. Abdou}, Chaos Solitons Fractals 33, No. 2, 513--522 (2007; Zbl 1133.35308) Full Text: DOI References: [1] Wadati, M.; Segur, H.; Ablowitz, M. J., J Phys Soc Jpn, 61, 1187 (1992) [2] Wadati, M.; Sanuki, H.; Konno, K., Prof Theor Phys, 53, 419 (1975) [3] Wadati, M., J Phys, 57, 5-6, 841-847 (2001) [4] Wadati, M., J Phys Soc Jpn, 32, 1681 (1972) [5] Drazin, P. G.; Johnson, R. S., Solitons: an introduction (1989), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0661.35001 [6] Debtnath, L., Nonlinear partial differential equations for scientist and engineers (1997), Birkhauser: Birkhauser Boston [7] Adomian, G., The decomposition method (1994), Kluwer Acad. Publ.: Kluwer Acad. Publ. Boston · Zbl 0803.35020 [8] Adomian, G.; Serrano, S. E., Appl Math Lett, 11, 53 (1998) [9] Adomian, G.; Rach, R.; Shawagfeh, N. T., Phys Lett, 2, 161 (1995) [10] Deeba, E. Y.; Khuri, S. A., J Comput Phys, 124, 442 (1996) [11] Oldham, K. B.; Spanier, J., The fractional calculus (1974), Academic Press: Academic Press New York · Zbl 0428.26004 [12] Podlubny, I., Fractional differential equation (1999), Academic Press: Academic Press New York · Zbl 0893.65051 [13] Tian, L.; Yin, J., Chaos, Solitons & Fractals, 23, 159 (2004) [14] Momoni, S., Chaos, Solitons & Fractals, 28, 930 (2006) [15] Wazwaz, A. M., Chaos, Solitons & Fractals, 13, 321 (2002) [16] Wazwaz, A. M., Appl Math Comput, 11, 33 (2000) [17] ElWakil SA, Abdou MA, Elhanbaly A. Adomian decomposition method for solving the diffusion-convection reaction equations, Appl Math and Comput, in press.; ElWakil SA, Abdou MA, Elhanbaly A. Adomian decomposition method for solving the diffusion-convection reaction equations, Appl Math and Comput, in press. [18] Abdou, M. A., JQSRT, 95, 407 (2005) [19] Kaya, D.; El-Sayed, M., Phys Lett A, 313, 82 (2003) [20] Seng, V.; Abbaoui, K. Y., Math Comput Model, 24, 59 (1996) [21] Lesnic, D., Chaos, Solitons & Fractals, 28, 776 (2006) [22] Feng, X., Phys Lett A, 213, 167 (1996) [23] Billingham, J., Nonlinearity, 17, 313 (2004) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.