Symmetric Radial Basis Function Method for Simulation of Elliptic Partial Differential Equations
by
Phatiphat Thounthong 1
, 
Muhammad Nawaz Khan 2, Iltaf Hussain 2, Imtiaz Ahmad 2 and 
Poom Kumam 3,*
Phatiphat Thounthong 1, Muhammad Nawaz Khan 2, Iltaf Hussain 2, Imtiaz Ahmad 2 and Poom Kumam 3,*
1
Renewable Energy Research Centre & Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand
2
Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
3
KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
*
Author to whom correspondence should be addressed.
Mathematics 2018, 6(12), 327; https://doi.org/10.3390/math6120327
Received: 8 October 2018 / Revised: 28 November 2018 / Accepted: 8 December 2018 / Published: 14 December 2018
(This article belongs to the Special Issue Numerical Methods for Partial Differential Equations)
In this paper, the symmetric radial basis function method is utilized for the numerical solution of two- and three-dimensional elliptic PDEs. Numerical results are obtained by using a set of uniform or random points. Numerical tests are accomplished to demonstrate the efficacy and accuracy of the method on both regular and irregular domains. Furthermore, the proposed method is tested for the solution of elliptic PDE in the case of various frequencies.
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Keywords:
meshless method; radial basis function; Poisson equation; Helmholtz equation; irregular domains
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MDPI and ACS Style
Thounthong, P.; Khan, M.N.; Hussain, I.; Ahmad, I.; Kumam, P. Symmetric Radial Basis Function Method for Simulation of Elliptic Partial Differential Equations. Mathematics 2018, 6, 327.
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