A New Variational Iteration Method for a Class of Fractional Convection-Diffusion Equations in Large Domains

Mohammad Abolhasani, Saeid Abbasbandy and Tofigh Allahviranloo
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Mohammad Abolhasani: Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran 14778, Iran
Saeid Abbasbandy: Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran 14778, Iran
Tofigh Allahviranloo: Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran 14778, Iran

Mathematics, 2017, vol. 5, issue 2, 1-15

Abstract: In this paper, we introduced a new generalization method to solve fractional convection–diffusion equations based on the well-known variational iteration method (VIM) improved by an auxiliary parameter. The suggested method was highly effective in controlling the convergence region of the approximate solution. By solving some fractional convection–diffusion equations with a propounded method and comparing it with standard VIM, it was concluded that complete reliability, efficiency, and accuracy of this method are guaranteed. Additionally, we studied and investigated the convergence of the proposed method, namely the VIM with an auxiliary parameter. We also offered the optimal choice of the auxiliary parameter in the proposed method. It was noticed that the approach could be applied to other models of physics.

Keywords: auxiliary parameter; fractional convection–diffusion equation; variational iteration method (VIM) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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