Symmetric Radial Basis Function Method for Simulation of Elliptic Partial Differential Equations

Phatiphat Thounthong, Muhammad Nawaz Khan, Iltaf Hussain, Imtiaz Ahmad and Poom Kumam
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Phatiphat Thounthong: 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
Muhammad Nawaz Khan: Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
Iltaf Hussain: Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
Imtiaz Ahmad: Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
Poom Kumam: 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

Mathematics, 2018, vol. 6, issue 12, 1-12

Abstract: 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.

Keywords: meshless method; radial basis function; Poisson equation; Helmholtz equation; irregular domains (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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