Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions
Fractional calculus and applied analysis, Tome 9 (2006) no. 4, pp. 333-349
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In this paper, a space fractional diffusion equation (SFDE) with nonhomogeneous
boundary conditions on a bounded domain is considered. A
new matrix transfer technique (MTT) for solving the SFDE is proposed.
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. Analytic solutions of the SFDE are derived.
Finally, some numerical results are given to demonstrate that the MTT is
a computationally efficient and accurate method for solving SFDE.
Keywords:
Fractional Diffusion, Anomalous Diffusion, Non-Homogeneous Boundary Conditions, Numerical Approximation, 26A33, 35S15
@article{FCAA_2006_9_4_a1,
author = {Ilic, M. and Liu, F. and Turner, I. and Anh, V.},
title = {Numerical {Approximation} of a {Fractional-In-Space} {Diffusion} {Equation} {(II)} {\textendash} with {Nonhomogeneous} {Boundary} {Conditions}},
journal = {Fractional calculus and applied analysis},
pages = {333--349},
publisher = {mathdoc},
volume = {9},
number = {4},
year = {2006},
language = {en},
url = {http://geodesic.mathdoc.fr/item/FCAA_2006_9_4_a1/}
}
TY - JOUR AU - Ilic, M. AU - Liu, F. AU - Turner, I. AU - Anh, V. TI - Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions JO - Fractional calculus and applied analysis PY - 2006 SP - 333 EP - 349 VL - 9 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FCAA_2006_9_4_a1/ LA - en ID - FCAA_2006_9_4_a1 ER -
%0 Journal Article %A Ilic, M. %A Liu, F. %A Turner, I. %A Anh, V. %T Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions %J Fractional calculus and applied analysis %D 2006 %P 333-349 %V 9 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/FCAA_2006_9_4_a1/ %G en %F FCAA_2006_9_4_a1
Ilic, M.; Liu, F.; Turner, I.; Anh, V. Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions. Fractional calculus and applied analysis, Tome 9 (2006) no. 4, pp. 333-349. http://geodesic.mathdoc.fr/item/FCAA_2006_9_4_a1/