3 papers
math.NA2022
A fast two-level Strang splitting method for multi-dimensional spatial fractional Allen-Cahn equations with discrete maximum principle
Yao-Yuan Cai, Zhi-Wei Fang, Hao Chen +1
In this paper, we study the numerical solutions of the multi-dimensional spatial fractional Allen-Cahn equations. After semi-discretization for the spatial fractional Riesz derivat…
math.NA2021
Fast second-order evaluation for variable-order Caputo fractional derivative with applications to fractional sub-diffusion equations
Jia-li Zhang, Zhi-wei Fang, Hai-wei Sun
In this paper, we propose a fast second-order approximation to the variable-order (VO) Caputo fractional derivative, which is developed based on - formula and the exponent…
math.NA2021
Exponential-sum-approximation technique for variable-order time-fractional diffusion equations
Jia-Li Zhang, Zhi-Wei Fang, Hai-Wei Sun
In this paper, we study the variable-order (VO) time-fractional diffusion equations. For a VO function , we develop an exponential-sum-approximation (ESA) technique t…