Related papers: Stability Problems in Symbolic Integration
Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of…
All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as…
Finite element plate and shell formulations are ubiquitous in structural analysis for modeling all kinds of slender structures, both for static and dynamic analyses. The latter are particularly challenging as the high order nature of the…
A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…
This paper introduces the concept of dimensional stability for spline spaces over T-meshes, providing the first mathematical definition and a preliminary classification framework. We define dimensional stability as an invariant within the…
Stochastic switched systems are a relevant class of stochastic hybrid systems with probabilistic evolution over a continuous domain and control-dependent discrete dynamics over a finite set of modes. In the past few years several different…
The connection of function properties of solutions with exponential stability of linear impulsive differential equation $$\dot{x} (t) - \sum_{k=1}^m {A_k (t) x[h_k(t)]} = r(t),~ t \geq 0, x(\xi ) = \varphi (\xi),~ \xi < 0,$$ $$x(\tau_j) =…
We consider a class of differential-algebraic equations (DAEs) with index zero in an infinite dimensional Hilbert space. We define a space of consistent initial values, which lead to classical continuously differential solutions for the…
We present several topics involving the computation of dynamical systems. The emphasis is on work in progress and the presentation is informal -- there are many technical details which are not fully discussed. The topics are chosen to…
Physics-based animation of soft or rigid bodies for real-time applications often suffers from numerical instabilities. We analyse one of the most common sources of unwanted behaviour: the numerical integration strategy. To assess the impact…
We continue the study of stabilization phenomena for Dynkin diagram sequences initiated in the earlier work of Kleber and the present author. We consider a more general class of sequences than that of this earlier work, and isolate a…
The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) are re-examined in the light of the recently introduced concept of global stability of…
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…
In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the…
Stable event structures, and their duality with prime algebraic domains arising as partial orders of configurations, are a landmark of concurrency theory, providing a clear characterisation of causality in computations. They have been used…
We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…
Symbolic summation as an active research topic of symbolic computation provides efficient algorithmic tools for evaluating and simplifying different types of sums arising from mathematics, computer science, physics and other areas. Most of…
This paper presents a guided tour of some specific problems encountered in the stability analysis of linear dynamical systems including delays in their systems' representation. More precisely, we will address the characterization of…
The paper focuses on the numerical stability and accuracy of implicit time-domain integration (TDI) methods when applied for the solution of a power system model impacted by time delays. Such a model is generally formulated as a set of…