Two meshless methods based on pseudo spectral delta-shaped basis functions and barycentric rational interpolation for numerical solution of modified Burgers equation

Abstract

In this paper, we solve modified Burgers equation numerically. Time discretization for modified Burgers equation is made by using finite difference approach along with a linearization technique. For space discretization, we propose two meshless approachs. One of them is based on delta-shaped basis functions-pseudo spectral method and the other is based on barycentric rational interpolation method. To see performance of the proposed methods, two test problems are investigated and obtained results are compared with other studies available in literature such as finite element, wavelet and some collocation methods. Accurate results are obtained using fewer collocation points. Further, von Neumann method has been used to discuss the stability of the methods. The comparisons show the applicability of suggested two methods.

Keywords:

• Delta-shaped basis functions-pseudo spectral method
• Barycentric rational interpolation method
• modified burgers equation
• Numerical solution
• nonlinear PDE

2010 Mathematics Subject Classifications:

• 65M70
• 65N35

Acknowledgments

The author wants to convey his thanks to the editor in charge and anonymous reviewers whose comments and suggestions improve this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Ömer Oruç  http://orcid.org/0000-0002-6655-3543