4 citations · 5 across the 4 of their papers we have counts for
4 papers
An Operator Learning Approach via Function-valued Reproducing Kernel Hilbert Space for Differential Equations
Kaijun Bao, Xu Qian, Ziyuan Liu +1
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this en…
Two regularized energy-preserving finite difference methods for the logarithmic Klein-Gordon equation
Jingye Yan, Xu Qian, Hong Zhang +1
We present and analyze two regularized finite difference methods which preserve energy of the logarithmic Klein-Gordon equation (LogKGE). In order to avoid singularity caused by th…
Regularized finite difference methods for the logarithmic Klein-Gordon equation
Jingye Yan, Hong Zhang, Xu Qian +1
We propose and analyze two regularized finite difference methods for the logarithmic Klein-Gordon equation (LogKGE). Due to the blowup phenomena caused by the logarithmic nonlinear…
Mass and energy conservative high order diagonally implicit Runge--Kutta schemes for nonlinear Schrödinger equation in one and two dimensions
Ziyuan Liu, Hong Zhang, Xu Qian +1
We present and analyze a series of conservative diagonally implicit Runge--Kutta schemes for the nonlinear Schrödiner equation. With the application of the newly developed invarian…