Batiha, B.; Noorani, M. S. M.; Hashim, I. Numerical simulation of the generalized Huxley equation by He’s variational iteration method. (English) Zbl 1118.65367 Appl. Math. Comput. 186, No. 2, 1322-1325 (2007). Summary: By means of the variational iteration method the solution of a generalized Huxley equation is obtained, a comparison with the Adomian decomposition method is made, showing that the former is more effective than the later. J.-H. He’s variational iteration method [Int. J. Non-Linear Mech. 34, No. 4, 699–708 (1999; Zbl 1342.34005)] is introduced to overcome the difficulty arising in calculating Adomian polynomials. Cited in 32 Documents MSC: 65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs 35Q72 Other PDE from mechanics (MSC2000) Keywords:Huxley equation; Adomian decomposition method; variational iteration method; Lagrange multiplier Citations:Zbl 1342.34005 PDFBibTeX XMLCite \textit{B. Batiha} et al., Appl. Math. Comput. 186, No. 2, 1322--1325 (2007; Zbl 1118.65367) Full Text: DOI References: [1] Wang, X. Y.; Zhu, Z. S.; Lu, Y. K., Solitary wave solutions of the generalized Burgers-Huxley equation, Phys. Lett. A, 23, 271-274 (1990) · Zbl 0708.35079 [2] I. Hashim, M.S.M. Noorani, B. Batiha, A note on the Adomian decomposition method for the generalized Huxley equation, Appl. Math. Comput., in press. doi:10.1016/j.amc.2006.03.011.; I. Hashim, M.S.M. Noorani, B. Batiha, A note on the Adomian decomposition method for the generalized Huxley equation, Appl. Math. Comput., in press. doi:10.1016/j.amc.2006.03.011. · Zbl 1173.65340 [3] Wazwaz, A. M., Travelling wave solutions of generalized forms of Burgers, Burgers-KdV and Burgers-Huxley equations, Appl. Math. Comput., 169, 639-656 (2005) · Zbl 1078.35109 [4] Hashim, I.; Noorani, M. S.M.; Said Al-Hadidi, M. R., Solving the generalized Burgers-Huxley equation using the Adomian decomposition method, Math. Comput. Model, 43, 1404-1411 (2006) · Zbl 1133.65083 [5] Estevez, P. G., Non-classical symmetries and the singular modified Burger’s and Burger’s-Huxley equation, Phys. Lett. A, 27, 2113-2127 (1994) · Zbl 0838.35114 [6] He, J. H., A new approach to Nonlinear Partial Differential Equations, Comm. Nonlinear Sci. Numer. Simul., 2, 4, 230-235 (1997) [7] He, J. H., Variational iteration method – a kind of non-linear analytical technique: some examples, J. Non-linear Mech., 34, 699-708 (1999) · Zbl 1342.34005 [8] He, J. H., Variational iteration method for delay differential equations, Comm. Nonlinear Sci. Numer. Simul., 2, 4, 235-236 (1997) [9] Abdou, M. A.; Soliman, A. A., Variational iteration method for solving Burger’s and coupled Burger’s equation, J. Comput. Appl. Math., 181, 2, 245-251 (2005) · Zbl 1072.65127 [10] Momani, S.; Abuasad, S., Application of He’s variational iteration method to Helmholtz equation, Chaos, Soliton and Fractals, 27, 5, 1119-1123 (2006) · Zbl 1086.65113 [11] Soliman, A. A., A numerical simulation and explicit solutions of KdV-Burgers and Lax’s seventh-order KdV equation, Chaos, Soliton and Fractals, 29, 2, 294-302 (2006) · Zbl 1099.35521 [12] Inokuti, M.; Sekine, H.; Mura, T., General use of the Lagrange multiplier in nonlinear mathematical physics, (Nemat-Nassed, S., Variational Method in the Mechanics of Solids (1978), Pergamon Press), 156-162 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.