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Mathematics 2017, 5(2), 26; doi:10.3390/math5020026

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

Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran 14778, Iran
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Academic Editor: Lokenath Debnath
Received: 27 February 2017 / Revised: 15 April 2017 / Accepted: 27 April 2017 / Published: 11 May 2017
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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. View Full-Text
Keywords: auxiliary parameter; fractional convection–diffusion equation; variational iteration method (VIM) auxiliary parameter; fractional convection–diffusion equation; variational iteration method (VIM)
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Abolhasani, M.; Abbasbandy, S.; Allahviranloo, T. A New Variational Iteration Method for a Class of Fractional Convection-Diffusion Equations in Large Domains. Mathematics 2017, 5, 26.

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