Fawang Liu

A Crank–Nicolson ADI Galerkin–Legendre spectral method for the two-dimensional Riesz space distributed-order advection–diffusion equation

Publisher: Elsevier BV

Date: 11-2018

DOI: 10.1016/J.CAMWA.2018.08.042

A vertex-centred finite volume method for the 3D multi-term time and space fractional Bloch–Torrey equation with fractional Laplacian

Publisher: Elsevier BV

Date: 11-2022

DOI: 10.1016/J.CNSNS.2022.106666

An alternating direction implicit spectral method for solving two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations

Publisher: Elsevier BV

Date: 02-2019

DOI: 10.1016/J.APNUM.2018.10.005

Fractional diffusion model generalised by the distributed-order operator involving variable diffusion coefficients

Publisher: Australian Mathematical Publishing Association, Inc.

Date: 23-10-2023

DOI: 10.21914/ANZIAMJ.V64.17959

A study of distributed‐order time fractional diffusion models with continuous distribution weight functions

Publisher: Wiley

Date: 05-07-2022

DOI: 10.1002/NUM.22896

Abstract: The distributed‐order time fractional diffusion model with Dirichlet nonhomogeneous boundary conditions on a finite domain is considered. Four choices of continuous distribution weight functions with mean μ and standard deviation σ are investigated to study their impact on both the short‐time and long‐time solution behavior. An implicit numerical method implemented on a graded mesh is proposed to solve the model and the stability and convergence analysis are presented. Semi‐analytic solutions are also derived for these distributions to assess the accuracy of the scheme. Numerical results highlight that the four continuous distribution weight functions produce a short‐time solution behavior that is consistent with those solutions from the classical time fractional partial differential equation with fractional order γ * = μ . There are however long‐time differences in the solution behavior that become more distinguishable as σ increases. In particular, we find a smaller value of σ produces more diffuse profiles and the diffusion rate slows as σ increases. Furthermore, the asymptotic behavior of the solution may be influenced by the time‐fractional orders ranging between the smallest nonzero weight order and mean μ for the continuous uniform and raised cosine distribution weight functions, respectively. Similar findings are also observed for the truncated normal and beta distributions.

Reproducing kernel particle method for two-dimensional time-space fractional diffusion equations in irregular domains

Publisher: Elsevier BV

Date: 12-2018

DOI: 10.1016/J.ENGANABOUND.2018.10.002

Numerical solution of the time fractional Black-Scholes model governing European options

Publisher: Elsevier BV

Date: 05-2015

DOI: 10.1016/J.CAMWA.2016.02.007

Multi-term time-fractional Bloch equations and application in magnetic resonance imaging

Publisher: Elsevier BV

Date: 08-2017

DOI: 10.1016/J.CAM.2017.01.018

Discovery Projects - Grant ID: DP230102414

Start Date: 2023

End Date: 12-2025

Amount: $373,000.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP180103858

Start Date: 05-2018

End Date: 12-2021

Amount: $364,029.00

Funder: Australian Research Council

Discovery Projects - Grant ID: DP190101889

Start Date: 05-2019

End Date: 05-2023

Amount: $339,000.00

Funder: Australian Research Council