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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,…