On the effective method for the space-fractional advection-diffusion equation by the Galerkin method

Author:

Jebreen Haifa Bin1,Wang Hongzhou2

Affiliation:

1. Department of mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

2. Beijing Key Lab on Mathematical Characterization, Analysis, and Applications of Complex Information, MIIT Key Laboratory of Mathematical Theory and Computation in Information Security, School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China

Abstract

<p>The present work is dedicated to a study that focuses on solving space-fractional advection-diffusion equations (SFADEs) using the Galerkin method. Through our analysis, we demonstrate the effectiveness of this approach in solving the considered equations. After introducing the Chebyshev cardinal functions (CCFs), the Caputo fractional derivative (CFD) was represented based on these bases as an operational matrix. Applying the Galerkin method reduces the desired equation to a system of algebraic equations. We have proved that the method converges analytically. By solving some numerical examples, we have demonstrated that the proposed method is effective and yields superior outcomes compared to existing methods for addressing this problem.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

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