English

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

Numerical Analysis 2015-05-01 v1 Analysis of PDEs

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.

Keywords

Cite

@article{arxiv.1504.08178,
  title  = {Numerical method based on Galerkin approximation for the fractional advection-dispersion equation},
  author = {Harendra Singh and Manas Ranjan Sahoo and Om Prakash Singh},
  journal= {arXiv preprint arXiv:1504.08178},
  year   = {2015}
}