×

Numerical simulation of the generalized Huxley equation by He’s variational iteration method. (English) Zbl 1118.65367

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.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q72 Other PDE from mechanics (MSC2000)

Citations:

Zbl 1342.34005
PDF BibTeX XML Cite
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. · 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, (), 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.