Preprint Essay Version 1 This version is not peer-reviewed

An Efficient Local Formulation for Time-Dependent PDEs

Version 1 : Received: 30 January 2019 / Approved: 31 January 2019 / Online: 31 January 2019 (14:27:34 CET)

A peer-reviewed article of this Preprint also exists.

Ahmad, I.; Ahsan, M.; Din, Z.-U.; Masood, A.; Kumam, P. An Efficient Local Formulation for Time–Dependent PDEs. Mathematics 2019, 7, 216. Ahmad, I.; Ahsan, M.; Din, Z.-U.; Masood, A.; Kumam, P. An Efficient Local Formulation for Time–Dependent PDEs. Mathematics 2019, 7, 216.

Journal reference: Mathematics 2019, 7, 216
DOI: 10.3390/math7030216

Abstract

In this paper, a local meshless method (LMM) based on radial basis functions (RBFs) is utilized for the numerical solution of various types of PDEs, due to the flexibility with respect to geometry and high order of convergence rate. In case of global meshless methods, the two major deficiencies are the computational cost and the optimum value of shape parameter. Therefore, research is currently focus towards localized radial basis function approximations, as the local meshless method is proposed here. The local meshless procedures is used for spatial discretization whereas for temporal discretization different time integrators are employed. The proposed local meshless method is testified in terms of efficiency, accuracy and ease of implementation using regular and irregular domains.

Subject Areas

Local meshless method, RBFs, Irregular domains, Kortewege-de Vries types equations, reaction-diffusion Brusselator system.

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