Collocation Finite Element Method for the Fractional Fokker–Planck Equation

IF 1.7 4区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

International Journal for Numerical Methods in Fluids Pub Date : 2024-10-13 DOI:10.1002/fld.5343

Hatice Karabenli, Alaattin Esen, Yusuf Uçar

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Abstract

In this study, the approximate results of the fractional Fokker–Planck equations have been investigated. First, finite element schemes have been obtained using collocation finite element method based on the trigonometric quintic B-spline basis functions. Then, the present method is tested on two fundamental problems having appropriate initial conditions. The newly obtained numerical results contained the error norms $L_{2}$ and $L_{\infty}$ for various temporal and spatial steps are compared with the exact ones and other solutions. More accurate results have been obtained for large numbers of spatial and temporal elements.

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来源期刊

International Journal for Numerical Methods in Fluids 物理-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

111

审稿时长

8 months

期刊介绍： The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.