1 citations · 1 across the 1 of their papers we have counts for
4 papers
Mass-preserving spatio-temporal adaptive PINN for Cahn-Hilliard equations with strong nonlinearity and singularity
Qiumei Huang, Jiaxuan Ma, Zhen Xu
As one kind of important phase field equations, Cahn-Hilliard equations involve high-order spatial derivatives, strong nonlinearities, and even solution singularities when certain…
Exponential Runge-Kutta methods of collocation type for parabolic equations with time-dependent delay
Qiumei Huang, Alexander Ostermann, Gangfan Zhong
In this paper, exponential Runge-Kutta methods of collocation type (ERKC) which were originally proposed in (Appl Numer Math 53:323-339, 2005) are extended to semilinear parabolic…
Exponential Runge-Kutta methods for parabolic equations with state-dependent delay
Qiumei Huang, Alexander Ostermann, Gangfan Zhong
The aim of this paper is to construct and analyze exponential Runge-Kutta methods for the temporal discretization of a class of semilinear parabolic problems with arbitrary state-d…
Nonsmooth data error estimates for exponential Runge-Kutta methods and applications to split exponential integrators
Qiumei Huang, Alexander Ostermann, Gangfan Zhong
We derive error bounds for exponential Runge-Kutta discretizations of parabolic equations with nonsmooth initial data. Our analysis is carried out in a framework of abstract semili…