Project dates: 01/01/2008 - Ongoing
The research on variable-order fractional models is relatively new, and numerical approximation of these models is still at an early stage of development. In various applications in science and engineering, such as Cardiac science, biology and hydrogeology, the concept of a variable-order operator has been developed to more accurately describe the evolution of the underlying system.
Chief Investigators
Team
Publications
- F. Liu*, P. Zhuang, I. Turner, V. Anh and K. Burrage (2014) Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model. IEEE Explore Conference Proceedings, Italy
- H. Zhang, F. Liu*, P. Zhuang, I. Turner and V. Anh (2014) Numerical analysis of a new space-time variable fractional order advection-dispersion equation. Applied Mathematics and Computation
- S. Chen, F. Liu* and K. Burrage (2014) Numerical simulation of a new two-dimensional variable-order fractional percolation equation in non-homogeneous porous media. Computers and Mathematics with Applications
- Chen, Chang-Ming, Liu, Fawang, Turner, Ian, Anh, Vo, Chen, Y. (2013) Numerical approximation for a variable-order nonlinear reaction–subdiffusion equation. Numerical Algorithms, 63 (2), pp.265-290.
- Shen, S., Liu, Fawang, Anh, Vo, Turner, Ian, Chen, J. (2013) A characteristic difference method for the variable-order fractional advection-diffusion equation. Journal of Applied Mathematics and Computing, 42 (1 - 2), pp.371-386.
- Chen, Chang-Ming, Liu, Fawang, Burrage, Kevin, Chen, Y. (2013) Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative. IMA Journal of Applied Mathematics, 78 (5), pp.924-944.
- Shen, Shujun, Liu, Fawang, Chen, Jing, Turner, Ian, Anh, Vo (2012) Numerical techniques for the variable order time fractional diffusion equation. Applied Mathematics and Computation, 218 (22), pp.10861-10870.
- Chen, Chang-Ming, Liu, Fawang, Anh, Vo, Turner, Ian (2012) Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation. Mathematics of Computation, 81 (277), pp.345-366.
- Chen, Chang-Ming, Liu, Fawang, Turner, Ian, Anh, Vo (2011) Numerical methods with fourth-order spatial accuracy for variable-order nonlinear Stokes' first problem for a heated generalized second grade fluid. Computers and Mathematics with Applications, 62 (3), pp.971-986.
- Chen, Chang-Ming, Liu, Fawang, Anh, Vo, Turner, Ian (2011) Numerical simulation for the variable-order Galilei invariant advection diffusion equation with a nonlinear source term. Applied Mathematics and Computation, 217 (12), pp.5729-5742.
- Chen, Chang-Ming, Liu, Fawang, Burrage, Kevin (2011) Numerical analysis for a variable-order nonlinear cable equation. Journal of Computational and Applied Mathematics, 236 (2), pp.209-224.
- Chen, Chang-Ming, Liu, Fawang, Anh, Vo, Turner, Ian (2010) Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equations. SIAM Journal on Computing, 32 (4), pp.1740-1760.
- Zhuang, Pinghui, Liu, Fawang, Anh, Vo, Turner, Ian (2009) Numerical methods for the variable-order fractional advection-diffusion equation with a nonlinear source term. SIAM Journal on Numerical Analysis, 47 (3), pp.1760-1781.
- Lin, R, Liu, Fawang, Anh, Vo, Turner, Ian (2009) Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation. Applied Mathematics and Computation, 212 (2), pp.435-445.
