Numerical simulation of partial differential equations via local meshless method
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Publication Details
Author list: Ahmad I., Riaz M., Ayaz M., Arif M., Islam S., Kumam P.
Publisher: MDPI AG
Publication year: 2019
Volume number: 11
Issue number: 2
ISSN: 2073-8994
eISSN: 2073-8994
Languages: English-Great Britain (EN-GB)
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Abstract
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. ฉ 2018 by the authors.
Keywords
Black-Scholes PDE model, Coupled Drinfeld's-Sokolov-Wilson equations, Kortewege-de Vries-Burgers' equation, Linear diffusion equation, Non rectangular domains, Regularized long wave equation
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