Numerical simulation of PDEs by local meshless differential quadrature collocation method
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Publication Details
Author list: Ahmad I., Ahsan M., Hussain I., Kumam P., Kumam W.
Publisher: MDPI AG
Publication year: 2019
Volume number: 11
Issue number: 3
ISSN: 2073-8994
eISSN: 2073-8994
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, a local meshless differential quadrature collocation method based on radial basis functions is proposed for the numerical simulation of one-dimensional Klein-Gordon, two-dimensional coupled Burgers', and regularized long wave equations. Both local and global meshless collocation procedures are used for spatial discretization, which convert the mentioned partial differential equations into a system of ordinary differential equations. The obtained system has been solved by the forward Euler difference formula. An upwind technique is utilized in the case of the convection-dominated coupled Burgers' model equation. Having no need for the mesh in the problem domain and being less sensitive to the variation of the shape parameter as compared to global meshless methods are the salient features of the local meshless method. Both rectangular and non-rectangular domains with uniform and scattered nodal points are considered. Accuracy, efficacy, and the ease of implementation of the proposed method are shown via test problems. ฉ 2019 by the authors.
Keywords
An upwind technique, Differential quadrature, Meshless method, Radial basis functions
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