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Journal of Applied Mathematics
Volume 2018, Article ID 3416860, 18 pages
Research Article

Numerical Solution to Coupled Burgers’ Equations by Gaussian-Based Hermite Collocation Scheme

1Faculty of Science Environment and Energy, King Mongkut’s University of Technology North Bangkok (Rayong Campus), Rayong 21120, Thailand
2School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000, Thailand
3Centre of Excellence in Mathematics, Bangkok 10400, Thailand

Correspondence should be addressed to Sayan Kaennakham;

Received 8 May 2018; Revised 21 August 2018; Accepted 4 September 2018; Published 27 September 2018

Academic Editor: Mustafa Inc

Copyright © 2018 Nissaya Chuathong and Sayan Kaennakham. 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.


One of the most challenging PDE forms in fluid dynamics namely Burgers equations is solved numerically in this work. Its transient, nonlinear, and coupling structure are carefully treated. The Hermite type of collocation mesh-free method is applied to the spatial terms and the 4th-order Runge Kutta is adopted to discretize the governing equations in time. The method is applied in conjunction with the Gaussian radial basis function. The effect of viscous force at high Reynolds number up to 1,300 is investigated using the method. For the purpose of validation, a conventional global collocation scheme (also known as “Kansa” method) is applied parallelly. Solutions obtained are validated against the exact solution and also with some other numerical works available in literature when possible.