Numerical Approximation of a Fractional-In-Space Diffusion Equation, I

Ilic, M., et al. "Numerical Approximation of a Fractional-In-Space Diffusion Equation, I." Fractional Calculus and Applied Analysis 8.3 (2005): 323-341. <http://eudml.org/doc/11303>.

@article{Ilic2005,
abstract = {2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary)This paper provides a new method and corresponding numerical schemes to approximate a fractional-in-space diffusion equation on a bounded domain under boundary conditions of the Dirichlet, Neumann or Robin type. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Numerical results are provided to gauge the performance of the proposed method relative to exact analytical solutions determined using a spectral representation of the fractional derivative. Initial results for a variety of one-dimensional test problems appear promising. Furthermore, the proposed strategy can be generalised to higher dimensions.* This research was partially supported by the Australian Research Council grant LP0348653.},
author = {Ilic, M., Liu, F., Turner, I., Anh, V.},
journal = {Fractional Calculus and Applied Analysis},
keywords = {26A33; 35S15},
language = {eng},
number = {3},
pages = {323-341},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Numerical Approximation of a Fractional-In-Space Diffusion Equation, I},
url = {http://eudml.org/doc/11303},
volume = {8},
year = {2005},
}

TY - JOUR
AU - Ilic, M.
AU - Liu, F.
AU - Turner, I.
AU - Anh, V.
TI - Numerical Approximation of a Fractional-In-Space Diffusion Equation, I
JO - Fractional Calculus and Applied Analysis
PY - 2005
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 8
IS - 3
SP - 323
EP - 341
AB - 2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary)This paper provides a new method and corresponding numerical schemes to approximate a fractional-in-space diffusion equation on a bounded domain under boundary conditions of the Dirichlet, Neumann or Robin type. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Numerical results are provided to gauge the performance of the proposed method relative to exact analytical solutions determined using a spectral representation of the fractional derivative. Initial results for a variety of one-dimensional test problems appear promising. Furthermore, the proposed strategy can be generalised to higher dimensions.* This research was partially supported by the Australian Research Council grant LP0348653.
LA - eng
KW - 26A33; 35S15
UR - http://eudml.org/doc/11303
ER -