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Numerical Method Based on Galerkin Approximation for the Fractional Advection-Dispersion Equation

Abstract

In this paper, we present a numerical method for solving homogeneous as well as non-homogeneous fractional advection-dispersion equation (FADE). The numerical method is based on the Galerkin approximation. The Galerkin approximation converts the FADE into a system of fractional ordinary differential equations whose solutions is discussed. Convergence of the proposed method is shown. Numerical examples are given and numerical results are compared with exact solution to show the effectiveness and accuracy of the proposed method.

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Acknowledgments

The author is very grateful to the referees for their constructive comments and suggestions for the improvement of the paper. This paper is dedicated in the memory of Late Professor Om Prakash Singh who is one of the co-author of this article.

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Correspondence to Harendra Singh.

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Singh, H., Sahoo, M.R. & Singh, O.P. Numerical Method Based on Galerkin Approximation for the Fractional Advection-Dispersion Equation. Int. J. Appl. Comput. Math 3, 2171–2187 (2017). https://doi.org/10.1007/s40819-016-0233-0

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  • DOI: https://doi.org/10.1007/s40819-016-0233-0

Keywords

  • Fractional order advection-dispersion equation
  • Galerkin approximation
  • System of fractional order ODE
  • Convergence analysis

Mathematics Subject Classification

  • 35Q99
  • 65N99
  • 65D99