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Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

Ilic, Milos, Liu, Fawang, Turner, Ian, & Anh, Vo (2006) Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions. Fractional Calculus and Applied Analysis, 9(4), pp. 333-349.

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    Abstract

    In this paper, a space fractional di®usion equation (SFDE) with non-homogeneous 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 e±cient and accurate method for solving SFDE.

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    ID Code: 23835
    Item Type: Journal Article
    Additional URLs:
    Keywords: Fractional Diffusion, Anomalous Diffusion, Numercial Approximation, Homogenous Boundary Conditions
    ISSN: 1311-0454
    Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
    Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
    Deposited On: 18 Jun 2009 00:10
    Last Modified: 01 Mar 2012 10:05

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