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


Autoria(s): Ilic, M.; Liu, F.; Turner, I.; Anh, V.
Data(s)

29/08/2010

29/08/2010

2006

Resumo

2000 Mathematics Subject Classification: 26A33 (primary), 35S15

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.

* This research was partially supported by the Australian Research Council, Grant LP0348653 and the National Natural Science Foundation of China, Grant 10271098.

Identificador

Fractional Calculus and Applied Analysis, Vol. 9, No 4, (2006), 333p-349p

1311-0454

http://hdl.handle.net/10525/1287

Idioma(s)

en

Publicador

Institute of Mathematics and Informatics Bulgarian Academy of Sciences

Palavras-Chave #Fractional Diffusion #Anomalous Diffusion #Non-Homogeneous Boundary Conditions #Numerical Approximation #26A33 #35S15
Tipo

Article