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Numerical solution of a biological population model using He’s variational iteration method. (English) Zbl 1137.92033

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 J.-H. He, Int. J. Non-Linear Mech. 34, No. 4, 699–708 (1999; Zbl 1342.34005)] and the Adomian decomposition method [see G. Adomian and 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:

92D40 Ecology
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35K65 Degenerate parabolic equations
92D25 Population dynamics (general)
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