Numerical Approximation of Fractional Burgers Equation

Authors

  • A. Guesmia Université du 20 Aoí»t 1955 - Skikda, Route d'El-Hadaiek, B.P. 26 - Skikda - 21000
  • N. Daili F. Abbas University, Faculty of Sciences, Department of Mathematics, 19000 Sétif, Algeria; 7650, rue Querbes, \# 15, Montréal, Québec, H3N 2B6, Canada

DOI:

https://doi.org/10.26713/cma.v1i2.114

Keywords:

Fractional Burgers equation, Finite volume methods, Approximations

Abstract

The mathematical modeling of physical and chemical systems is used extensively throughout science, engineering and applied mathematics. In order to make use of mathematical models, it is necessary to have solutions to the model equations. Generally, this requires numerical methods because of the complexity and number of equations. In this paper, we study and approximate a nonlinear fractional Burgers problem by finite volume schemes of order one in space and also in time. The purpose is to show that they converge to the solution of the considered problem and to establish error estimates. We prove that the finite volume schemes converge to weak entropic solutions as the discretization parameters tend to zero.

Downloads

Download data is not yet available.

Downloads

CITATION

How to Cite

Guesmia, A., & Daili, N. (2010). Numerical Approximation of Fractional Burgers Equation. Communications in Mathematics and Applications, 1(2), 77–90. https://doi.org/10.26713/cma.v1i2.114

Issue

Vol. 1 No. 2 (2010)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.