We discuss the modelling framework of port-Hamiltonian descriptor systems and their use in
numerical simulation and control. The structure is ideal for automated network-based …

We give a systematic method for discretizing Hamiltonian partial differential equations
(PDEs) with constant symplectic structure, while preserving their energy exactly. The same …

We present several essential improvements to the powerful scalar auxiliary variable (SAV)
approach. Firstly, by using the introduced scalar variable to control both the nonlinear and …

Recently, a new family of integrators (Hamiltonian Boundary Value Methods) has been
introduced, which is able to precisely conserve the energy function of polynomial …

Nonlinear Partial Differential Equations (PDEs) have become increasingly important in the
description of physical phenomena. Unlike Ordinary Differential Equations, PDEs can be …

Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous
Dynamical Systems A Concise Introduction to Geometric Numerical Integration presents the …

We propose a modification of collocation methods extending the 'averaged vector field
method'to high order. These new integrators exactly preserve energy for Hamiltonian …

The differential equation (DE) approach for convex optimization, which relates optimization
methods to specific continuous DEs with rate-revealing Lyapunov functionals, has gained …

In recent years, the numerical solution of differential problems, possessing constants of
motion, has been attacked by imposing the vanishing of a corresponding line integral. The …

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 …