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Open AccessArticle

Numerical Simulation of Partial Differential Equations via Local Meshless Method

1
Department of Mathematics, University of Swabi, Khyber Pakhtunkhwa 23200, Pakistan
2
Department of Mathematics, Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa 23200, Pakistan
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KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
4
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
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(2), 257; https://doi.org/10.3390/sym11020257
Received: 11 January 2019 / Revised: 12 February 2019 / Accepted: 14 February 2019 / Published: 19 February 2019
(This article belongs to the Special Issue Differential and Difference Equations and Symmetry)
In this paper, numerical simulation of one, two and three dimensional partial differential equations (PDEs) are obtained by local meshless method using radial basis functions (RBFs). Both local and global meshless collocation procedures are used for spatial discretization, which convert the given PDEs into a system of ODEs. Multiquadric, Gaussian and inverse quadratic RBFs are used for spatial discretization. The obtained system of ODEs has been solved by different time integrators. The salient feature of the local meshless method (LMM) is that it does not require mesh in the problem domain and also far less sensitive to the variation of shape parameter as compared to the global meshless method (GMM). Both rectangular and non rectangular domains with uniform and scattered nodal points are considered. Accuracy, efficacy and ease implementation of the proposed method are shown via test problems. View Full-Text
Keywords: radial basis functions; non rectangular domains; Kortewege-de Vries-Burgers’ equation; coupled Drinfeld’s-Sokolov-Wilson equations; regularized long wave equation; linear diffusion equation; Black-Scholes PDE model radial basis functions; non rectangular domains; Kortewege-de Vries-Burgers’ equation; coupled Drinfeld’s-Sokolov-Wilson equations; regularized long wave equation; linear diffusion equation; Black-Scholes PDE model
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MDPI and ACS Style

Ahmad, I.; Riaz, M.; Ayaz, M.; Arif, M.; Islam, S.; Kumam, P. Numerical Simulation of Partial Differential Equations via Local Meshless Method. Symmetry 2019, 11, 257. https://doi.org/10.3390/sym11020257

AMA Style

Ahmad I, Riaz M, Ayaz M, Arif M, Islam S, Kumam P. Numerical Simulation of Partial Differential Equations via Local Meshless Method. Symmetry. 2019; 11(2):257. https://doi.org/10.3390/sym11020257

Chicago/Turabian Style

Ahmad, Imtiaz; Riaz, Muhammad; Ayaz, Muhammad; Arif, Muhammad; Islam, Saeed; Kumam, Poom. 2019. "Numerical Simulation of Partial Differential Equations via Local Meshless Method" Symmetry 11, no. 2: 257. https://doi.org/10.3390/sym11020257

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