Related papers: Stability Problems on D-finite Functions
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
In this paper, we establish several improved Caffarelli-Kohn-Nirenberg and Hardy-type inequalities. Our main results are divided into two parts. In the first part, we consider the following Caffarelli-Kohn-Nirenberg inequality:…
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…
The sunflower equation describes the motion of the tip of a plant due to the auxin transportation under the influence of gravity. This work proposes the fractional-order generalization to this delay differential equation. The equation…
Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…
This paper considers linear delay-difference equations, that is, equations relating the state at a given time with its past values over a given bounded interval. After providing a well-posedness result and recalling Hale--Silkowski…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
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…
We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation…
This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large…
This report addresses the boundary value problem for a second-order linear singularly perturbed FIDE. Traditional methods for solving these equations often face stability issues when dealing with small perturbation parameters. We propose an…
Stability of time domain integral equation (TDIE) solvers has remained an elusive goal for many years. Advancement of this research has largely progressed on four fronts: (1) Exact integration, (2) Lubich quadrature, (3) smooth temporal…
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…
In this article we discuss the role of stability functions in geometric invariant theory and apply stability function techniques to problems in toric geometry. In particular we show how one can use these techniques to recover results of…
We consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest…
We develop and analyze a stabilization term for cut finite element approximations of an elliptic second order partial differential equation on a surface embedded in $\mathbb{R}^d$. The new stabilization term combines properly scaled normal…
The stability for the viscosity solutions of a differential equation with a perturbation term added to the Infinity-Laplace Operator is studied. This is the so-called Infinity-Laplace Equation with variable exponent infinity. An…
We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of…
In this paper, we study planar polygonal curves from the variational methods. We show an unified interpretation of discrete curvatures and the Steiner-type formula by extracting the notion of the discrete curvature vector from the first…