Related papers: Fully Conservative Difference Schemes for the Rota…
We introduce a family of fourth order two-step methods that preserve the energy function of canonical polynomial Hamiltonian systems. Each method in the family may be viewed as a correction of a linear two-step method, where the correction…
We consider the geometric numerical integration of Hamiltonian systems subject to both equality and "hard" inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. We…
In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model…
We consider Novikov's Camassa-Holm type equation with cubic nonlinearity. In particular, we present a compact parametric representation of the smooth bright multisolution solutions on a constant background and investigate their structure.…
We consider in this paper a numerical approximation of Poisson-Nernst-Planck-Navier- Stokes (PNP-NS) system. We construct a decoupled semi-discrete and fully discrete scheme that enjoys the properties of positivity preserving, mass…
Port-Hamiltonian (PH) systems provide a framework for modeling, analysis and control of complex dynamical systems, where the complexity might result from multi-physical couplings, non-trivial domains and diverse nonlinearities. A major…
A new class of semi-implicit numerical schemes for linear advection equation on Cartesian grids is derived that is inspired by so-called $\kappa$-schemes used with fully explicit discretizations for this type of problems. Opposite to fully…
We perform a numerical analysis of a class of randomly perturbed {H}amiltonian systems and {P}oisson systems. For the considered additive noise perturbation of such systems, we show the long time behavior of the energy and quadratic…
Nonlinear contact dynamics are widely regarded as intrinsically nonlinear systems whose behaviour depends strongly on geometry and impact conditions. Here we show that any one-dimensional conservative contact system satisfying monotone…
Many important physical systems can be described as the evolution of a Hamiltonian system, which has the important property of being conservative, that is, energy is conserved throughout the evolution. Physics Informed Neural Networks and…
We exhibit a sufficient condition in terms of decay at infinity of the initial data for the finite time blowup of strong solutions to the Camassa--Holm equation: a wave breaking will occur as soon as the initial data decay faster at…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the skew-symmetric structure of the Hamiltonian form of the…
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
In this paper, a class of arbitrarily high-order linear momentum-preserving and energy-preserving schemes are proposed, respectively, for solving the regularized long-wave equation. For the momentum-preserving scheme, the key idea is based…
Given a first order dynamical system possessing a commutative algebra of dynamical symmetries, we show that, under certain conditions, there exists a Poisson structure on an open neighbourhood of its regular (not necessarily compact)…
In this paper, we consider a class of stochastic midpoint and trapezoidal Lawson schemes for the numerical discretization of highly oscillatory stochastic differential equations. These Lawson schemes incorporate both the linear drift and…
In this paper, we develop a provably energy stable and conservative discontinuous spectral element method for the shifted wave equation in second order form. The proposed method combines the advantages and central ideas of very successful…
In the article, we discuss the conservation laws for the nonlinear Schr\"{o}dinger equation with wave operator under multisymplectic integrator (MI). First, the conservation laws of the continuous equation are presented and one of them is…