10 citations · 11 across the 5 of their papers we have counts for
6 papers
An accurate parallel finite difference method for the variable-order fractional Laplacian in heterogeneous media
Shiping Zhou, Yanzhi Zhang
Anomalous diffusion in heterogeneous media is ubiquitous across physical and biological systems, where spatially varying microstructures give rise to distinct transport regimes. Va…
Modeling Unknown Nonlocal PDE Systems via Flow Map Learning
Zhongshu Xu, Ying Li, Yanzhi Zhang +1
Nonlocal partial differential equations arise in many applications but are often difficult to model and learn because of the presence of nonlocal operators. We present a flow-map l…
Variable-order fractional Laplacian and its accurate and efficient computations with meshfree methods
Yixuan Wu, Yanzhi Zhang
The variable-order fractional Laplacian plays an important role in the study of heterogeneous systems. In this paper, we propose the first numerical methods for the variable-order…
Gaussian radial basis functions collocation for fractional PDEs: methodology and error analysis
Xiaochuan Tian, Yixuan Wu, Yanzhi Zhang
The paper introduces a new meshfree pseudospectral method based on Gaussian radial basis functions (RBFs) collocation to solve fractional Poisson equations. Hypergeometric function…
Fourier pseudospectral methods for the spatial variable-order fractional wave equations
Yanzhi Zhang, Xiaofei Zhao, Shiping Zhou
In this paper, we propose Fourier pseudospectral methods to solve the variable-order space fractional wave equation and develop an accelerated matrix-free approach for its effectiv…
A novel and simple spectral method for nonlocal PDEs with the fractional Laplacian
Shiping Zhou, Yanzhi Zhang
We propose a novel and simple spectral method based on the semi-discrete Fourier transforms to discretize the fractional Laplacian . Numerical analysis and experime…