Related papers: The stability of the Nystr\"om method for double l…
The aim of this paper is to prove the existence and smoothness of stable and unstable invariant manifolds for a stochastic delayed partial differential equation of parabolic type. The stochastic delayed partial differential equation is…
Performing a stability analysis during the design of any electronic circuit is critical to guarantee its correct operation. A closed-loop stability analysis can be performed by analysing the impedance presented by the circuit at a…
The effect of rotation upon the classical two-layer Rayleigh-Taylor instability is considered theoretically and compared with previous experimental results. In particular we consider a two-layer system with an axis of rotation that is…
Given a complete, connected Riemannian manifold $ \mathbb{M}^n $ with Ricci curvature bounded from below, we discuss the stability of the solutions of a porous medium-type equation with respect to the 2-Wasserstein distance. We produce…
In this article we demonstrate and compare two modified versions of the classical finite section method for band-dominated operators in case the latter is not stable. For both methods we give explicit criteria for their applicability.
In this paper, we explore the stability of an inverted pendulum under a generalized parametric excitation described by a superposition of $N$ cosines with different amplitudes and frequencies, based on a simple stability condition that does…
A new criterion for A-stability of peer two-step methods is presented which is verifiable exactly in exact arithmetic by checking semi-definiteness of a certain test matrix. It depends on the existence of two positive definite weight…
We consider the implementation of the split-step method where the linear part of the nonlinear Schr\"odinger equation is solved using a finite-difference discretization of the spatial derivative. The von Neumann analysis predicts that this…
Stabilization is still a somewhat controversial issue concerning its very existence and also the precise conditions for its occurrence. The key quantity to settle these questions is the ionization probability, for which hitherto no…
In this paper we investigate the stability properties of the so-called gBBKS and GeCo methods, which belong to the class of nonstandard schemes and preserve the positivity as well as all linear invariants of the underlying system of…
The stability of two quantum counter-streaming electron beams is investigated within the quantum plasma fluid equations for arbitrarily oriented wave vectors. The analysis reveals that the two quantum two-stream unstable branches are indeed…
The incompressible smoothed particle hydrodynamics method (ISPH) is a numerical method widely used for accurately and efficiently solving flow problems with free surface effects. However, to date there has been little mathematical…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
Phase diagram of a two-dimensional system with a potential which stabilizes Kagome lattice is calculated. It is shown that this system demonstrate a set of crystalline and the regions of stability of these phases are calculated. The…
We find computable criteria for stability of symplectic leaves of Poisson manifolds. Using Poisson geometry as an inspiration, we also give a general criterion for stability of leaves of Lie algebroids, including singular ones. This not…
Incompressible flows of an ideal two-dimensional fluid on a closed orientable surface of positive genus are considered. Linear stability of harmonic, i.e. irrotational and incompressible, solutions to the Euler equations is shown using the…
The stability of liquid crystal phases in presence of small amount of non-mesogenic impurities is of general interest for a large spectrum of technological applications and in the theories of binary mixtures. Starting from the known phase…
Clustering with most objective functions is NP-Hard, even to approximate well in the worst case. Recently, there has been work on exploring different notions of stability which lend structure to the problem. The notion of stability,…
We propose a quantitative direct method to prove the local stability of a stationary solution for a rough differential equation and its regular discretization scheme. Using Doss-Sussmann technique and stopping time analysis, we provide…
Stability properties of the well-known Fourier split-step method used to simulate a soliton and similar solutions of the nonlinear Dirac equations, known as the Gross--Neveu model, are studied numerically and analytically. Three distinct…