4 citations · 6 across the 12 of their papers we have counts for
13 papers
A unified convergence analysis framework of the energy-stable ETDRK3 schemes for the No-slope-selection thin film model
Jingwei Sun, Haifeng Wang, Hong Zhang +2
This paper establishes a unified framework for the space-time convergence analysis of the energy-stable third-order accurate exponential time differencing Runge-Kutta schemes. By e…
An exponential-free Runge--Kutta framework for developing third-order unconditionally energy stable schemes for the Cahn--Hilliard equation
Haifeng Wang, Jingwei Sun, Hong Zhang +2
In this work, we develop a class of up to third-order energy-stable schemes for the Cahn--Hilliard equation. Building on Lawson's integrating factor Runge--Kutta method, which is w…
High-order and Mass-conservative Regularized Implicit-explicit relaxation Runge-Kutta methods for the logarithmic Schrödinger equation
Jingye Yan, Hong Zhang, Yabing Wei +1
The non-differentiability of the singular nonlinearity (such as ) at presents significant challenges in devising accurate and efficient numerical schemes for the…
Global-in-time energy stability: a powerful analysis tool for the gradient flow problem without maximum principle or Lipschitz assumption
J. Sun, H. Wang, H. Zhang +2
Before proving (unconditional) energy stability for gradient flows, most existing studies either require a strong Lipschitz condition regarding the non-linearity or certain $L^{\in…
SPFNO: Spectral operator learning for PDEs with Dirichlet and Neumann boundary conditions
Ziyuan Liu, Yuhang Wu, Daniel Zhengyu Huang +3
Neural operators have been validated as promising deep surrogate models for solving partial differential equations (PDEs). Despite the critical role of boundary conditions in PDEs,…
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…
Arbitrary high-order structure-preserving schemes for the generalized Rosenau-type equation
Chaolong Jiang, Xu Qian, Songhe Song +1
In this paper, we are concerned with arbitrarily high-order momentum-preserving and energy-preserving schemes for solving the generalized Rosenau-type equation, respectively. The d…
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…
Arbitrary high-order linear structure-preserving schemes for the regularized long-wave equation
Chaolong Jiang, Xu Qian, Songhe Song +1
In this paper, a class of arbitrarily high-order linear momentum-preserving and energy-preserving schemes are proposed, respectively, for solving the regularized long-wave equation…
High-order linearly implicit structure-preserving exponential integrators for the nonlinear Schrödinger equation
Chaolong Jiang, Jin Cui, Xu Qian +1
A novel class of high-order linearly implicit energy-preserving integrating factor Runge-Kutta methods are proposed for the nonlinear Schrödinger equation. Based on the idea of the…
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…