The Gegenbauer Wavelets-Based Computational Methods for the Coupled System of Burgers’ Equations with Time-Fractional Derivative

Neslihan Ozdemir, Aydin Secer and Mustafa Bayram
Additional contact information
Neslihan Ozdemir: Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34220, Turkey
Aydin Secer: Department of Mathematical Engineering, Yildiz Technical University, Istanbul 34220, Turkey
Mustafa Bayram: Department of Computer Engineering, Gelisim University, Istanbul 34315, Turkey

Mathematics, 2019, vol. 7, issue 6, 1-15

Abstract: In this study, Gegenbauer wavelets are used to present two numerical methods for solving the coupled system of Burgers’ equations with a time-fractional derivative. In the presented methods, we combined the operational matrix of fractional integration with the Galerkin method and the collocation method to obtain a numerical solution of the coupled system of Burgers’ equations with a time-fractional derivative. The properties of Gegenbauer wavelets were used to transform this system to a system of nonlinear algebraic equations in the unknown expansion coefficients. The Galerkin method and collocation method were used to find these coefficients. The main aim of this study was to indicate that the Gegenbauer wavelets-based methods is suitable and efficient for the coupled system of Burgers’ equations with time-fractional derivative. The obtained results show the applicability and efficiency of the presented Gegenbaur wavelets-based methods.

Keywords: Gegenbauer wavelets; coupled Burgers’ equations; operational matrix of fractional integration; Galerkin method; collocation method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/6/486/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/6/486/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:6:p:486-:d:234917

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().