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

Ilic, M.;  Liu, F.;  Turner, I.;  Anh, V. — 2005

Fractional Calculus and Applied Analysis

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...

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

Ilic, M.;  Liu, F.;  Turner, I.;  Anh, V. — 2006

Fractional Calculus and Applied Analysis

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...

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