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In this paper, a space fractional diffusion 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… (More)

The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). In this work, an explicit finite-difference scheme for TFDE is presented. Discrete models of a non-Markovian random walk are generate for simulating random variables… (More)

- P. Zhuang, Fawang Liu, Vo V. Anh, Ian W. Turner
- SIAM J. Numerical Analysis
- 2008

(2008) New solution and analytical techniques of the implicit numerical method for the anomalous subdiffusion equation. Notice: Changes introduced as a result of publishing processes such as copy-editing and formatting may not be reflected in this document. For a definitive version of this work, please refer to the published source: Abstract. A… (More)

- P. Zhuang, Fawang Liu, Vo V. Anh, Ian W. Turner
- SIAM J. Numerical Analysis
- 2009

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moveover, we also present a fractional method of lines, a matrix transfer technique, and an… (More)

- Fawang Liu, P. Zhuang, Vo V. Anh, Ian W. Turner, Kevin Burrage
- Applied Mathematics and Computation
- 2007

- Chang-Ming Chen, Fawang Liu, Vo V. Anh, Ian W. Turner
- SIAM J. Scientific Computing
- 2010

- Q. Liu, Fawang Liu, Ian W. Turner, Vo V. Anh
- J. Comput. Physics
- 2007

Approximation of the Levy–Feller advection–dispersion process by random walk and finite difference method. Notice: Changes introduced as a result of publishing processes such as copy-editing and formatting may not be reflected in this document. For a definitive version of this work, please refer to the published source: Abstract In this paper we present a… (More)

- Jennifer A Thackham, D L Sean McElwain, Ian W Turner
- Bulletin of mathematical biology
- 2009

In the wound healing process, the cell movement associated with chemotaxis generally outweighs the movement associated with random motion, leading to advection-dominated mathematical models of wound healing. The equations in these models must be solved with care, but often inappropriate approaches are adopted. Two one-dimensional test problems arising from… (More)

- Fanhai Zeng, Changpin Li, Fawang Liu, Ian W. Turner
- SIAM J. Scientific Computing
- 2013

In this paper, two finite difference/element approaches for the time-fractional sub-diffusion equation with Dirichlet boundary conditions are developed, in which the time direction is approximated by the fractional linear multistep method and the space direction is approximated by the finite element method. The two methods are unconditionally stable and… (More)

- M. ILIĆ, I. W. TURNER, D. P. SIMPSON
- 2007

In this paper, we investigate a method for restarting the Lanczos method for approximating the matrix-vector product f (A)b, where A ∈ R n×n is a symmetric matrix. For analytic f we derive a novel restart function that identifies the error in the Lanczos approximation. The restart procedure is then generated by a restart formula using a sequence of these… (More)