A spectral Galerkin method for the fractional order diffusion and wave equation

A spectral Galerkin method for the fractional order diffusion and wave equation Int J Adv Eng Sci Appl Math https://doi.org/10.1007/s12572-018-0208-y IIT, Madras A spectral Galerkin method for the fractional order diffusion and wave equation 1 1 Thomas Camminady Martin Frank Indian Institute of Technology Madras 2018 Abstract We are going to present a suitable bases to treat This has shown to be especially useful in e.g biology [1], the space- and timefractional diffusion equation with the within quantum physics [2], for chemical reactions [3], in Galerkin method to obtain spectral convergence in both, stock market prediction [4], in epidemic models [5] and time and space. Furthermore, by carefully choosing a many more. All the above shall motivate a reconsideration Fourier ansatz in space, we can guarantee the resulting of the classical random walk model. matrices to be sparse, even though fractional order differ- The classical diffusion equation can be derived via ential equations are global operator. This is due to the fact several ways as presented in the literature. To derive the that the chosen basis consists of eigenfunctions of the given fractional diffusion equation, it is useful to reconsider the fractional differential operator. Numerical experiments random walk approach, used to derive the standard diffu- validate the theoretically predicted spectral convergence http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Advances in Engineering Sciences and Applied Mathematics Springer Journals

A spectral Galerkin method for the fractional order diffusion and wave equation

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Publisher
Springer India
Copyright
Copyright © 2018 by Indian Institute of Technology Madras
Subject
Engineering; Engineering, general; Mathematical and Computational Engineering
ISSN
0975-0770
eISSN
0975-5616
D.O.I.
10.1007/s12572-018-0208-y
Publisher site
See Article on Publisher Site

Abstract

Int J Adv Eng Sci Appl Math https://doi.org/10.1007/s12572-018-0208-y IIT, Madras A spectral Galerkin method for the fractional order diffusion and wave equation 1 1 Thomas Camminady Martin Frank Indian Institute of Technology Madras 2018 Abstract We are going to present a suitable bases to treat This has shown to be especially useful in e.g biology [1], the space- and timefractional diffusion equation with the within quantum physics [2], for chemical reactions [3], in Galerkin method to obtain spectral convergence in both, stock market prediction [4], in epidemic models [5] and time and space. Furthermore, by carefully choosing a many more. All the above shall motivate a reconsideration Fourier ansatz in space, we can guarantee the resulting of the classical random walk model. matrices to be sparse, even though fractional order differ- The classical diffusion equation can be derived via ential equations are global operator. This is due to the fact several ways as presented in the literature. To derive the that the chosen basis consists of eigenfunctions of the given fractional diffusion equation, it is useful to reconsider the fractional differential operator. Numerical experiments random walk approach, used to derive the standard diffu- validate the theoretically predicted spectral convergence

Journal

International Journal of Advances in Engineering Sciences and Applied MathematicsSpringer Journals

Published: Jun 4, 2018

References

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