Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions

Ilic, M., et al. "Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions." Fractional Calculus and Applied Analysis 9.4 (2006): 333-349. <http://eudml.org/doc/11286>.

@article{Ilic2006,
abstract = {2000 Mathematics Subject Classification: 26A33 (primary), 35S15In 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.* This research was partially supported by the Australian Research Council, Grant LP0348653 and the National Natural Science Foundation of China, Grant 10271098.},
author = {Ilic, M., Liu, F., Turner, I., Anh, V.},
journal = {Fractional Calculus and Applied Analysis},
keywords = {26A33; 35S15},
language = {eng},
number = {4},
pages = {333-349},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions},
url = {http://eudml.org/doc/11286},
volume = {9},
year = {2006},
}

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
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 9
IS - 4
SP - 333
EP - 349
AB - 2000 Mathematics Subject Classification: 26A33 (primary), 35S15In 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.* This research was partially supported by the Australian Research Council, Grant LP0348653 and the National Natural Science Foundation of China, Grant 10271098.
LA - eng
KW - 26A33; 35S15
UR - http://eudml.org/doc/11286
ER -