Eur. Phys. J. Plus (2018) 133: 335
https://doi.org/10.1140/epjp/i2018-12191-x

Regular Article

On the numerical evaluation for studying the fractional KdV, KdV-Burgers and Burgers equations

¹ Department of Mathematics and Statistics, College of Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
² Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
³ Department of Mathematics, College of Arts and Sciences, Najran University, Najran, Saudi Arabia
⁴ Department of Mathematics, Faculty of Applied Science, Taiz University, Taiz, Yemen

^* e-mail: khaledma_sd@hotmail.com

Received: 23 March 2018
Accepted: 11 July 2018
Published online: 24 August 2018

Abstract

This paper is devoted to present an accurate numerical procedure to solve fractional (Caputo sense) Korteweg-de Vries, Korteweg-de Vries-Burgers and Burgers equations by using the spectral Chebyshev collocation method and finite difference method (FDM). The proposed problem is reduced to a system of ODEs with the help of the properties of Chebyshev polynomials of the third kind. This system is solved by using the FDM. Some theorems about the convergence analysis are stated and proved. A numerical simulation and a comparison with the previous work are presented.