113 citations · 302 across the 23 of their papers we have counts for
9 papers · 1 filter
The use of a time-fractional transport model for performing computational homogenisation of 2D heterogeneous media exhibiting memory effects
Libo Feng, Ian Turner, Patrick Perre +1
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-d…
The reflectionless properties of Toeplitz waves and Hankel waves: an analysis via Bessel functions
Kevin Burrage, Pamela Burrage, Shev MacNamara
We study reflectionless properties at the boundary for the wave equation in one space dimension and time, in terms of a well-known matrix that arises from a simple discretisation o…
A discrete least squares collocation method for two-dimensional nonlinear time-dependent partial differential equations
Fanhai Zeng, Ian Turner, Kevin Burrage +1
In this paper, we develop regularized discrete least squares collocation and finite volume methods for solving two-dimensional nonlinear time-dependent partial differential equatio…
Efficient multistep methods for tempered fractional calculus: Algorithms and Simulations
Ling Guo, Fanhai Zeng, Ian Turner +2
In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative opera…
Computational modelling of cardiac ischaemia using a variable-order fractional Laplacian
Megan E. Farquhar, Timothy J. Moroney, Qianqian Yang +2
Heart failure is one of the most common causes of death in the western world. Many heart problems are linked to disturbances in cardiac electrical activity, such as wave re-entry c…
A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations
Fanhai Zeng, Ian Turner, Kevin Burrage +1
We propose a new class of semi-implicit methods for solving nonlinear fractional differential equations and study their stability. Several versions of our new schemes are proved to…