4 citations · 5 across the 5 of their papers we have counts for
6 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…
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…