2 citations · 3 across the 4 of their papers we have counts for
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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…
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…
Double-activation neural network for solving parabolic equations with time delay
Qiumei Huang, Qiao Zhu
This paper presents the double-activation neural network (DANN), a novel network architecture designed for solving parabolic equations with time delay. In DANN, each neuron is equi…
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…