140 citations · 245 across the 19 of their papers we have counts for
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FNWoS: Fractional Neural Walk-on-Spheres Methods for High-Dimensional PDEs Driven by -stable Lévy Process on Irregular Domains
Ling Guo, Mingxin Qin, Changtao Sheng +2
In this paper, we develop a highly parallel and derivative-free fractional neural walk-on-spheres method (FNWoS) for solving high-dimensional fractional Poisson equations on irregu…
Fast time-stepping discontinuous Galerkin method for the subdiffusion equation
Hui Zhang, Fanhai Zeng, Xiaoyun Jiang +1
The nonlocality of the fractional operator causes numerical difficulties for long time computation of the time-fractional evolution equations. This paper develops a high-order fast…
Splitting physics-informed neural networks for inferring the dynamics of integer- and fractional-order neuron models
Simin Shekarpaz, Fanhai Zeng, George Karniadakis
We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs). The propose…
Bi-orthogonal fPINN: A physics-informed neural network method for solving time-dependent stochastic fractional PDEs
Lei Ma, Rong xin Li, Fanhai Zeng +2
Fractional partial differential equations (FPDEs) can effectively represent anomalous transport and nonlocal interactions. However, inherent uncertainties arise naturally in real a…
Analysis of a Backward Euler-type Scheme for Maxwell's Equations in a Havriliak-Negami Dispersive Medium
Yubo Yang, Li-Lian Wang, Fanhai Zeng
For the Maxwell's equations in a Havriliak-Negami (H-N) dispersive medium, the associated energy dissipation law has not been settled at both continuous level and discrete level. I…
Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations
Hui Zhang, Fanhai Zeng, Xiaoyun Jiang +1
In 1986, Dixon and McKee developed a discrete fractional Grönwall inequality [Z. Angew. Math. Mech., 66 (1986), pp. 535--544], which can be seen as a generalization of the classica…
Optimal order finite element approximations for variable-order time-fractional diffusion equations
Xiangcheng Zheng, Fanhai Zeng, Hong Wang
We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are prove…
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…
A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations
Hui Zhang, Xiaoyun Jiang, Fanhai Zeng +1
The reaction-diffusion model can generate a wide variety of spatial patterns, which has been widely applied in chemistry, biology, and physics, even used to explain self-regulated…
Numerical analysis of linear and nonlinear time-fractional subdiffusion equations
Yubo Yang, Fanhai Zeng
In this paper, a new type of the discrete fractional Gr{ö}nwall inequality is developed, which is applied to analyze the stability and convergence of a Galerkin spectral method for…
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…
An alternating direction implicit spectral method for solving two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations
Zeting Liu, Fawang Liu, Fanhai Zeng
In this paper, we consider the initial boundary value problem of the two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations. An alternating directi…
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…
On the analysis of mixed-index time fractional differential equation systems
Kevin Burrage, Pamela M. Burrage, Ian W. Turner +1
In this paper we study the class of mixed-index time fractional differential equations in which different components of the problem have different time fractional derivatives on th…
A stable fast time-stepping method for fractional integral and derivative operators
Fanhai Zeng, Ian Turner, Kevin Burrage
A unified fast time-stepping method for both fractional integral and derivative operators is proposed. The fractional operator is decomposed into a local part with memory length $Δ…
Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions
Fanhai Zeng, Zhongqiang Zhang, George Em Karniadakis
Starting with the asymptotic expansion of the error equation of the shifted Grünwald--Letnikov formula, we derive a new modified weighted shifted Grünwald--Letnikov (WSGL) formula…
Implicit-Explicit difference schemes for nonlinear fractional differential equations with non-smooth solutions
Wanrong Cao, Fanhai Zeng, Zhongqiang Zhang +1
We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order . From the known structure of th…
Second-order Stable Finite Difference Schemes for the Time-fractional Diffusion-wave Equation
Fanhai Zeng
We propose two stable and one conditionally stable finite difference schemes of second-order in both time and space for the time-fractional diffusion-wave equation. In the first sc…
Fractional differentiation matrices with applications
Fanhai Zeng, Changpin Li
In this paper, the fractional differential matrices based on the Jacobi-Gauss points are derived with respect to the Caputo and Riemann-Liouville fractional derivative operators. T…