83 citations · 320 across the 12 of their papers we have counts for
12 papers
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…
Fast implicit difference schemes for time-space fractional diffusion equations with the integral fractional Laplacian
Xian-Ming Gu, Hai-Wei Sun, Yanzhi Zhang +1
In this paper, we develop two fast implicit difference schemes for solving a class of variable-coefficient time-space fractional diffusion equations with integral fractional Laplac…
Numerical simulations for the energy-supercritical nonlinear wave equation
Jason Murphy, Yanzhi Zhang
We carry out numerical simulations of the defocusing energy-supercritical nonlinear wave equation for a range of spherically-symmetric initial conditions. We demonstrate numericall…
Numerical approximations for the tempered fractional Laplacian: Error analysis and applications
Siwei Duo, Yanzhi Zhang
In this paper, we propose an accurate finite difference method to discretize the -dimensional (for ) tempered integral fractional Laplacian and apply it to study the tem…
Accurate numerical methods for two and three dimensional integral fractional Laplacian with applications
Siwei Duo, Yanzhi Zhang
In this paper, we propose accurate and efficient finite difference methods to discretize the two- and three-dimensional fractional Laplacian () in hype…
A comparative study on nonlocal diffusion operators related to the fractional Laplacian
Siwei Duo, Hong Wang, Yanzhi Zhang
In this paper, we study four nonlocal diffusion operators, including the fractional Laplacian, spectral fractional Laplacian, regional fractional Laplacian, and peridynamic operato…
Computing the ground and first excited states of the fractional Schrodinger equation in an infinite potential well
Siwei Duo, Yanzhi Zhang
In this paper, we numerically study the ground and first excited states of the fractional Schrodinger equation in an infinite potential well. Due to the non-locality of the fractio…
An efficient spectral method for computing dynamics of rotating two-component Bose--Einstein condensates via coordinate transformation
Ming Ju, Qinglin Tang, Yanzhi Zhang
In this paper, we propose an efficient and accurate numerical method for computing the dynamics of rotating two-component Bose--Einstein condensates (BECs) which is described by co…
A simple and efficient numerical method for computing the dynamics of rotating Bose-Einstein condensates via a rotating Lagrangian coordinate
Weizhu Bao, Daniel Marahrens, Qinglin Tang +1
We propose a simple, efficient and accurate numerical method for simulating the dynamics of rotating Bose-Einstein condensates (BECs) in a rotational frame with/without a long-rang…
Dynamics of vortices in weakly interacting Bose-Einstein condensates
Alexander Klein, Dieter Jaksch, Yanzhi Zhang +1
We study the dynamics of vortices in ideal and weakly interacting Bose-Einstein condensates using a Ritz minimization method to solve the two-dimensional Gross-Pitaevskii equation.…