Numerical solution of a biological population model using He’s variational iteration method

Abstract

This paper presents numerical solution of a degenerate parabolic equation arising in the spatial diffusion of biological populations. The variational iteration method and Adomian decomposition method 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, variational iteration method overcomes the difficulty arising in calculating the Adomian's polynomials which is an important advantage over the Adomian decomposition method.

Exact solutions of coupled burgers equation with time-and space-fractional derivative

“…Each definition uses Riemann-Liouville fractional integration and derivations of whole order. The difference between the two definitions lies in the order of evaluation Riemann-Louville fractional integral of order  is defined as [1], [4], [5], [6], [8], [13].…”

Numerical solution of two dimensional time fractional-order biological population model

“…Sakar et al [10] and Prakash et al [11] have made use of the variational iteration method to find numerical solutions of time-fractional Fornberg-Whitham equation and fractional coupled Burger's equation respectively. Shakeri et al [12] solved the two dimensional biological population model for the standard case when α = 1 by a variational iteration method. Recently, Srivastava et al [13] studied two dimensional time fractional-order biological population model by Fractional reduced differential transform method.…”

Numerical simulation based on meshless technique to study the biological population model

“…[2]. Shakeri and Dehghan obtained numerical solution of the model using He's variational iteration method [10].…”