Related papers: Stability theory for some scalar finite difference…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
For a stationary sequence that is regularly varying and associated we give conditions which guarantee that partial sums of this sequence, under normalization related to the exponent of regular variation, converge in distribution to a…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
Approximating nonlinear dynamics with a truncated perturbative expan- sion may be accurate for a while, but it in general breaks down at a long time scale that is one over the small expansion parameter. There are interesting occasions in…
The development of finite/fixed-time stable optimization algorithms typically involves study of specific problem instances. The lack of a unified framework hinders understanding of more sophisticated algorithms, e.g., primal-dual gradient…
The numerical approximation of incompressible fluid-structure interaction problems with Lagrange multiplier is generally based on strongly coupled schemes. This delivers unconditional stability but at the expense of solving a…
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative,…
We consider the discretization of a semilinear damped wave equation arising, for instance, in the modeling of gas transport in pipeline networks. For time invariant boundary data, the solutions of the problem are shown to converge…
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
We present a novel approach to the analysis of a full model of scalar modulation instability (MI) by means of a simple geometrical description in the power vs. frequency plane. This formulation allows to relate the shape of the MI gain to…
For data sets with similar features, for example highly correlated features, most existing stability measures behave in an undesired way: They consider features that are almost identical but have different identifiers as different features.…
A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…
A solution to a given equation is structurally stable if it suffers only an infinitesimal change when the equation (not the solution) is perturbed infinitesimally. We have found that structural stability can be used as a velocity selection…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…
As we all know, the Fourier transform is continuous in the weak sense of tempered distribution; this ensures the weak stability of Fourier pairs. This article investigates a stronger form of stability of the pair of homogeneous profiles…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
The need to smoothly cover a computational domain of interest generically requires the adoption of several grids. To solve the problem of interest under this grid-structure one must ensure the suitable transfer of information among the…
This paper studies the stability of velocity-pressure mixed approximations of the Stokes problem when different finite element (FE) spaces for each component of the velocity field are considered. We consider some new combinations of…