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Research Papers

The Transport Dynamics Induced by Riesz Potential in Modeling Fractional Reaction–Diffusion-Mechanics System

[+] Author and Article Information
S. Saha Ray

Department of Mathematics,
National Institute of Technology,
Rourkela 769008, India
e-mails: saharays@nitrkl.ac.in; santanusaharay@yahoo.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 17, 2017; final manuscript received July 11, 2017; published online November 1, 2017. Assoc. Editor: Dumitru Baleanu.

J. Comput. Nonlinear Dynam 13(2), 021005 (Nov 01, 2017) (8 pages) Paper No: CND-17-1223; doi: 10.1115/1.4037418 History: Received May 17, 2017; Revised July 11, 2017

This paper comprises of a finite difference method with implicit scheme for the Riesz fractional reaction–diffusion equation (RFRDE) by utilizing the fractional-centered difference for approximating the Riesz derivative, and consequently, we obtain an implicit scheme which is proved to be convergent and unconditionally stable. Also a novel analytical approximate method has been dealt with namely optimal homotopy asymptotic method (OHAM) to investigate the solution of RFRDE. The numerical solutions of RFRDE obtained by proposed implicit finite difference method have been compared with the solutions of OHAM and also with the exact solutions. The comparative study of the results establishes the accuracy and efficiency of the techniques in solving RFRDE. The proposed OHAM renders a simple and robust way for the controllability and adjustment of the convergence region and is applicable to solve RFRDE.

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Figures

Grahic Jump Location
Fig. 1

Comparison of graphs for the approximate solution and the exact solution obtained by implicit finite difference scheme of Eq. (1.1) at t = 5

Grahic Jump Location
Fig. 2

Comparison of graphs for the exact solution and the approximate solution obtained by implicit finite difference scheme of Eq. (1.1) at t = 8

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