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Mathematics 2019, 7(2), 113; https://doi.org/10.3390/math7020113

A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator

Department of Mathematics, Faculty of Art and Science, Muş Alparslan University, 49100 Muş, Turkey
Received: 27 November 2018 / Revised: 6 January 2019 / Accepted: 21 January 2019 / Published: 22 January 2019
(This article belongs to the Special Issue Numerical Methods for Partial Differential Equations)
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Abstract

An efficient technique is proposed to solve the one-dimensional Burgers’ equation based on multiquadric radial basis function (MQ-RBF) for space approximation and a Lie-Group scheme for time integration. The comparisons of the numerical results obtained for different values of kinematic viscosity are made with the exact solutions and the reported results to demonstrate the efficiency and accuracy of the algorithm. It is shown that the numerical solutions concur with existing results and the proposed algorithm is efficient and can be easily implemented. View Full-Text
Keywords: Burgers’ equation; meshless method; multiquadric radial basis function (MQ-RBF); Lie-group method Burgers’ equation; meshless method; multiquadric radial basis function (MQ-RBF); Lie-group method
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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).
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Seydaoğlu, M. A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator. Mathematics 2019, 7, 113.

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