The local meshless collocation method for solving 2D fractional Klein-Kramers dynamics equation on irregular domains
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 16 August 2021
Issue publication date: 3 January 2022
Abstract
Purpose
This study aims to propose a new numerical method for solving non-linear partial differential equations on irregular domains.
Design/methodology/approach
The main aim of the current paper is to propose a local meshless collocation method to solve the two-dimensional Klein-Kramers equation with a fractional derivative in the Riemann-Liouville sense, in the time term. This equation describes the sub-diffusion in the presence of an external force field in phase space.
Findings
First, the authors use two finite difference schemes to discrete temporal variables and then the radial basis function-differential quadrature method has been used to estimate the spatial direction. To discrete the time-variable, the authors use two different strategies with convergence orders
Originality/value
The proposed numerical technique is flexible for different computational domains.
Keywords
Acknowledgements
The authors would like to thank the anonymous reviewers for their careful reading and constructive comments to improve the quality of this work.
Citation
Abbaszadeh, M., Pourbashash, H. and Khaksar-e Oshagh, M. (2022), "The local meshless collocation method for solving 2D fractional Klein-Kramers dynamics equation on irregular domains", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 1, pp. 41-61. https://doi.org/10.1108/HFF-12-2020-0781
Publisher
:Emerald Publishing Limited
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