Numerical method based on Galerkin approximation for the fractional\n advection-dispersion equation

2015/04/30 by Harendra Singh, Singh, Harendra, Manas Ranjan Sahoo +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.1504.08178

openalex publication_date 2015/04/30 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We use a concept of weak asymptotic solution for homogeneous as well as\nnon-homogeneous fractional advection dispersion type equations. Using Legendre\nscaling functions as basis, a numerical method based on Galerkin approximation\nis proposed. This leads to a system of fractional ordinary differential\nequations whose solutions in turn give approximate solution for the\nadvection-dispersion equations of fractional order. Under certain assumptions\non the approximate solutions, it is shown that this sequence of approximate\nsolutions forms a weak asymptotic solution. Numerical examples are given to\nshow the effectiveness of the proposed method.\n

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