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

Author

Listed:
  • Muaz Seydaoğlu

    (Department of Mathematics, Faculty of Art and Science, Muş Alparslan University, 49100 Muş, Turkey)

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.

Suggested Citation

  • Muaz Seydaoğlu, 2019. "A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator," Mathematics, MDPI, vol. 7(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:113-:d:199793
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    References listed on IDEAS

    as
    1. Mukundan, Vijitha & Awasthi, Ashish, 2015. "Efficient numerical techniques for Burgers’ equation," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 282-297.
    2. Maryam Sarboland & Azim Aminataei, 2014. "On the Numerical Solution of One-Dimensional Nonlinear Nonhomogeneous Burgers’ Equation," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-15, April.
    3. Huantian Xie & Dingfang Li & Feng Li, 2013. "A New Numerical Method of Particular Solutions for Inhomogeneous Burgers’ Equation," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, July.
    4. Hajiketabi, M. & Abbasbandy, S. & Casas, F., 2018. "The Lie-group method based on radial basis functions for solving nonlinear high dimensional generalized Benjamin–Bona–Mahony–Burgers equation in arbitrary domains," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 223-243.
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