4 papers
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…