12 citations · 39 across the 15 of their papers we have counts for
15 papers
A fully discrete LBRFD-IPDG method for linear fourth-order parabolic equations
Hongying Huang, Hong Zhang, Yanming Zhang
We propose a fully discrete method for linear fourth-order parabolic equations with Dirichlet boundary conditions, combining an implicit LBRFD multistep scheme in time with a mixed…
Cell-average based neural network method for high dimensional parabolic differential equations
Hong Zhang, Hongying Huang, Jue Yan
In this paper, we introduce cell-average based neural network (CANN) method to solve high-dimensional parabolic partial differential equations. The method is based on the integral…
Render unto Numerics: Orthogonal Polynomial Neural Operator for PDEs with Non-periodic Boundary Conditions
Ziyuan Liu, Haifeng Wang, Hong Zhang +3
By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency th…
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…