Next Article in Journal
Confidence Intervals for Mean and Difference between Means of Normal Distributions with Unknown Coefficients of Variation
Previous Article in Journal
Lattices and Rational Points
Article Menu
Issue 3 (September) cover image

Export Article

Open AccessArticle
Mathematics 2017, 5(3), 38; https://doi.org/10.3390/math5030038

Variable Shape Parameter Strategy in Local Radial Basis Functions Collocation Method for Solving the 2D Nonlinear Coupled Burgers’ Equations

Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778, Iran
*
Author to whom correspondence should be addressed.
Received: 31 May 2017 / Revised: 10 July 2017 / Accepted: 12 July 2017 / Published: 21 July 2017
Full-Text   |   PDF [2118 KB, uploaded 21 July 2017]   |  

Abstract

This study aimed at investigating a local radial basis function collocation method (LRBFCM) in the reproducing kernel Hilbert space. This method was, in fact, a meshless one which applied the local sub-clusters of domain nodes for the approximation of the arbitrary field. For time-dependent partial differential equations (PDEs), it would be changed to a system of ordinary differential equations (ODEs). Here, we intended to decrease the error through utilizing variable shape parameter (VSP) strategies. This method was an appropriate way to solve the two-dimensional nonlinear coupled Burgers’ equations comprised of Dirichlet and mixed boundary conditions. Numerical examples indicated that the variable shape parameter strategies were more efficient than constant ones for various values of the Reynolds number. View Full-Text
Keywords: local meshless method; variable shape parameter (VSP); reproducing kernel space; 2D nonlinear coupled Burgers’ equations local meshless method; variable shape parameter (VSP); reproducing kernel space; 2D nonlinear coupled Burgers’ equations
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Nojavan, H.; Abbasbandy, S.; Allahviranloo, T. Variable Shape Parameter Strategy in Local Radial Basis Functions Collocation Method for Solving the 2D Nonlinear Coupled Burgers’ Equations. Mathematics 2017, 5, 38.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top