36 citations · 43 across the 5 of their papers we have counts for
5 papers
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…
Highly accurate operator factorization methods for the integral fractional Laplacian and its generalization
Yixuan Wu, Yanzhi Zhang
In this paper, we propose a new class of operator factorization methods to discretize the integral fractional Laplacian for . The main advantage of ou…
A universal solution scheme for fractional and classical PDEs
Yixuan Wu, Yanzhi Zhang
We propose a unified meshless method to solve classical and fractional PDE problems with for . The classical () and fractional () Laplac…
A unified meshfree pseudospectral method for solving both classical and fractional PDEs
John Burkardt, Yixuan Wu, Yanzhi Zhang
In this paper, we propose a meshfree method based on the Gaussian radial basis function (RBF) to solve both classical and fractional PDEs. The proposed method takes advantage of th…