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

A spectral Galerkin method for the fractional order diffusion and wave equation We are going to present a suitable bases to treat the space- and timefractional diffusion equation with the Galerkin method to obtain spectral convergence in both, time and space. Furthermore, by carefully choosing a Fourier ansatz in space, we can guarantee the resulting matrices to be sparse, even though fractional order differential equations are global operator. This is due to the fact that the chosen basis consists of eigenfunctions of the given fractional differential operator. Numerical experiments validate the theoretically predicted spectral convergence for smooth problems. Additionally, we show that this method is also capable of computing approximation of the solution of the wave equation by letting the order of the spatial and temporal derivative approach two arbitrarily close. 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

We are going to present a suitable bases to treat the space- and timefractional diffusion equation with the Galerkin method to obtain spectral convergence in both, time and space. Furthermore, by carefully choosing a Fourier ansatz in space, we can guarantee the resulting matrices to be sparse, even though fractional order differential equations are global operator. This is due to the fact that the chosen basis consists of eigenfunctions of the given fractional differential operator. Numerical experiments validate the theoretically predicted spectral convergence for smooth problems. Additionally, we show that this method is also capable of computing approximation of the solution of the wave equation by letting the order of the spatial and temporal derivative approach two arbitrarily close.

Journal

International Journal of Advances in Engineering Sciences and Applied MathematicsSpringer Journals

Published: Jun 4, 2018

References

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