相关论文: Numerical integrators that contract volume
Finite element discretization of time dependent problems also require effective time-stepping schemes. While implicit Runge-Kutta methods provide favorable accuracy and stability problems, they give rise to large and complicated systems of…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
On the basis of the previous work by Tang \& Zhang (Appl. Math. Comput. 323, 2018, p. 204--219), in this paper we present a more effective way to construct high-order symplectic integrators for solving second order Hamiltonian equations.…
Conservation properties of iterative methods applied to implicit finite volume discretizations of nonlinear conservation laws are analyzed. It is shown that any consistent multistep or Runge-Kutta method is globally conservative. Further,…
A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded…
This paper contains an error analysis of two randomized explicit Runge-Kutta schemes for ordinary differential equations (ODEs) with time-irregular coefficient functions. In particular, the methods are applicable to ODEs of Carath\'eodory…
The work deals with two major topics concerning the numerical analysis of Runge-Kutta-like (RK-like) methods, namely their stability and order of convergence. RK-like methods differ from additive RK methods in that their coefficients are…
This paper presents comprehensive studies on frequency response optimized integrators considering second order derivative regarding their numerical error, numerical stability and transient performance. Frequency domain error analysis is…
Quantum versions of the hydrogen atom and the harmonic oscillator are studied on non Euclidean spaces of dimension N. 2N-1 integrals, of arbitrary order, are constructed via a multi-dimensional version of the factorization method, thus…
Analyzing the properties of entanglement in many-particle spin-1/2 systems is generally difficult because the system's Hilbert space grows exponentially with the number of constituent particles, $N$. Fortunately, it is still possible to…
Measuring entanglement is a demanding task in the field of quantum computation and quantum information theory. Recently, some authors experimentally demonstrated an embedding quantum simulator, using it to efficiently measure two-qubit…
An error analysis of Runge-Kutta convolution quadrature based on Gauss methods applied to hyperbolic operators is given. The order of convergence relies heavily on the parity of the number of stages, a more favourable situation arising for…
Quantitative characterization of different entanglement detection criteria for bipartite systems is presented. We review the implication sequence of these criteria and then numerically estimate volume ratios between criteria non-violating…
The Kuramoto model, describing the synchronization dynamics of coupled oscillators, has been generalized in many ways over the past years. One recent extension of the model replaces the oscillators, originally characterized by a single…
In quantum many-body systems with kinetically constrained dynamics, the Hilbert space can split into exponentially many disconnected subsectors, a phenomenon known as Hilbert-space fragmentation. We study the interplay of such fragmentation…
We study the asymptotic dynamics of piecewise contracting maps defined on a compact interval. For maps that are not necessarily injective, but have a finite number of local extrema and discontinuity points, we prove the existence of a…
We give properties of strict pseudocontractions and demicontractions defined on a Hilbert space, which constitute wide classes of operators that arise in iterative methods for solving fixed point problems. In particular, we give necessary…
Numerical integration (NI) packages commonly used in scientific research are limited to returning the value of a definite integral at the upper integration limit, also commonly referred to as numerical quadrature. These quadrature…
Complex dynamical networks appear in a wide range of physical, biological, and engineering systems. The coupling of subsystems with varying time scales often results in multirate behavior. During the simulation of highly integrated…
Trigonometric time integrators are introduced as a class of explicit numerical methods for quasilinear wave equations. Second-order convergence for the semi-discretization in time with these integrators is shown for a sufficiently regular…