相关论文: A Novel Discriminant Approximation of Periodic Dif…

We investigate the periodic and stationary solutions of distribution-dependent stochastic differential equations. While generally, the semigroups associated with the equations are nonlinear, we show that the methods of weak convergence and…

This paper is devoted to provide some new results on Lyapunov type inequalities for the periodic boundary value problem at higher eigenvalues. Our main result is derived from a detailed analysis on the number and distribution of zeros of…

We analyze two types of summation-by-parts finite difference operators for approximating the second derivative with variable coefficient. The first type uses ghost points, while the second type does not use any ghost points. A previously…

In this paper, we introduce a novel indefinite summation $\sum_{t} f(t)$ (or antidifference $\Delta ^{-1}f(t) $ ) formula for any given function $f$. We apply the indefinite summation formula to calculate a particular solution to a…

A scheme for stabilizing stochastic approximation iterates by adaptively scaling the step sizes is proposed and analyzed. This scheme leads to the same limiting differential equation as the original scheme and therefore has the same…

We establish a link between the basic properties of the discriminant of periodic second-order differential equations and an elementary analysis of Herglotz functions. Some generalizations are presented using the language of self-adjoint…

For the ordinary differential equation (ODE) $\dot{x}(t) = f(t,x)$, $x(0) = x_0$, $t\geq 0$, $x\in R^d$, assume $f$ to be at least continuous in $t$ and locally Lipshitz in $x$, and if necessary, several times continuously differentiable in…

The problem of exactly differentiating a signal with bounded second derivative is considered. A class of differentiators is proposed, which converge to the derivative of such a signal within a fixed, i.e., a finite and uniformly bounded…

In this paper, we derive a new method for optimal $\ell^{1}$- and $\ell^2$-approximation of discrete signals on ${\mathbb N}_{0}$ whose entries can be represented as an exponential sum of finite length. Our approach employs Prony's method…

For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions…

In this paper an autonomous analytical system of ordinary differential equations is considered. For an asymptotically stable steady state x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when…

We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…

The paper studies numerical methods that preserve a Lyapunov function of a dynamical system, i.e. numerical approximations whose energy decreases, just like in the original differential equation. With this aim, a discrete gradient method is…

In this paper we investigate the existence and uniqueness of bounded, periodic and almost periodic solutions for second order differential equations involving reflection of the argument.The relationship between frequency modules of forced…

A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral…

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…

For a class of nonsmooth composite optimization problems with linear equality constraints, we utilize a Lyapunov-based approach to establish the global exponential stability of the primal-dual gradient flow dynamics based on the proximal…

A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact…

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…

This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…