It is challenging to numerically solve oscillatory Hamiltonian systems due to the stiffness of
the problems and the requirement of highly stable and energy-preserving schemes. The …

Spatial discretizations of time-dependent partial differential equations usually result in a
large system of semi-linear and stiff ordinary differential equations. Taking the structures into …

In this paper, we develop a fully discrete entropy preserving ADER-Discontinuous Galerkin
(ADER-DG) method. To obtain this desired result, we equip the space part of the method …

In this paper, a family of novel energy-preserving schemes are presented for numerically
solving highly oscillatory Hamiltonian systems. These schemes are constructed by using the …

For the general class of residual distribution (RD) schemes, including many finite element
(such as continuous/discontinuous Galerkin) and flux reconstruction methods, an approach …

We develop error-control based time integration algorithms for compressible fluid dynamics
(CFD) applications and show that they are efficient and robust in both the accuracy-limited …

The Deferred Correction (DeC) methods combined with the residual distribution (RD)
approach allow the construction of high order continuous Galerkin (cG) schemes avoiding …

For problems in image processing and many other fields, a large class of effective neural
networks has encoder-decoder-based architectures. Although these networks have shown …

Recently, relaxation methods have been developed to guarantee the preservation of a
single global functional of the solution of an ordinary differential equation. Here, we …

We develop a general framework for designing conservative numerical methods based on
summation by parts operators and split forms in space, combined with relaxation Runge …