10 citations · 11 across the 5 of their papers we have counts for
5 papers
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…