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arXiv · 1504.08178

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

Harendra Singh·Manas Ranjan Sahoo·Om Prakash Singh
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Abstract

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

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Harendra Singh, Manas Ranjan Sahoo, Om Prakash Singh. 2015-04-30. Numerical method based on Galerkin approximation for the fractional advection-dispersion equation. https://arxiv.org/abs/1504.08178

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