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Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation
Joint Authors
Source
Advances in Mathematical Physics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-12-07
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
Metzler et al.
introduced a fractional Fokker-Planck equation (FFPE) describing a subdiffusive behavior of a particle under the combined influence of external nonlinear force field and a Boltzmann thermal heat bath.
In this paper, we present an interval Shannon wavelet numerical method for the FFPE.
In this method, a new concept named “dynamic interval wavelet” is proposed to solve the problem that the numerical solution of the fractional PDE is usually sensitive to boundary conditions.
Comparing with the traditional wavelet defined in the interval, the Newton interpolator is employed instead of the Lagrange interpolation operator, so, the extrapolation points in the interval wavelet can be chosen dynamically to restrict the boundary effect without increase of the calculation amount.
In order to avoid unlimited increasing of the extrapolation points, both the error tolerance and the condition number are taken as indicators for the dynamic choice of the extrapolation points.
Then, combining with the finite difference technology, a new numerical method for the time fractional partial differential equation is constructed.
A simple Fokker-Planck equation is taken as an example to illustrate the effectiveness by comparing with the Grunwald-Letnikov central difference approximation (GL-CDA).
American Psychological Association (APA)
Mei, Shu-Li& Zhu, De-Hai. 2013. Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation. Advances in Mathematical Physics،Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-500883
Modern Language Association (MLA)
Mei, Shu-Li& Zhu, De-Hai. Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation. Advances in Mathematical Physics No. 2013 (2013), pp.1-12.
https://search.emarefa.net/detail/BIM-500883
American Medical Association (AMA)
Mei, Shu-Li& Zhu, De-Hai. Interval Shannon Wavelet Collocation Method for Fractional Fokker-Planck Equation. Advances in Mathematical Physics. 2013. Vol. 2013, no. 2013, pp.1-12.
https://search.emarefa.net/detail/BIM-500883
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-500883