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Zbl 1137.92033
Shakeri, Fatemeh; Dehghan, Mehdi
Numerical solution of a biological population model using He's variational iteration method. (English)
[J] Comput. Math. Appl. 54, No. 7-8, 1197-1209 (2007). ISSN 0898-1221

Summary: This paper presents a numerical solution of a degenerate parabolic equation arising in the spatial diffusion of biological populations. The variational iteration method [see {\it J.-H. He}, Int. J. Non-Linear Mech. 34, No.~4, 699--708 (1999; Zbl 05137891)] and the Adomian decomposition method [see {\it G. Adomian} and {\it R. Rach}, Nonlinear Anal., Theory Methods Appl. 23, No.~5, 615--619 (1994; Zbl 0810.34015)] are used for solving this equation and then numerical results are compared with each other, showing that the variational iteration method leads to more accurate results. Furthermore, the variational iteration method overcomes the difficulty arising in calculating the Adomian polynomials, which is an important advantage over the Adomian decomposition method.

MSC 2000:: *92D40 Ecology
65M99 Numerical methods for IVP of PDE
35K65 Parabolic equations of degenerate type
92D25 Population dynamics

Keywords: biological population equation; variational iteration method; Adomian decomposition method; adomian polynomials; analytical solution

Citations: Zbl 0810.34015; Zbl 05137891

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