Related papers: Numerical Stability and Catalan Numbers
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
Recent results in the literature provide computational evidence that stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth-order nonlinear dif- fusion, with typical examples like the…
This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…
Discrete time evolution of one-dimensional maps is embedded in continuous time by truncating the Taylor series expansion of the time evolution operator to a finite order N. Truncations with N > 4 leads to unconditional instability.…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
We consider numerical instability that can be observed in simulations of localized solutions of the generalized nonlinear Schr\"odinger equation (NLS) by a split-step method where the linear part of the evolution is solved by a…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
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 studies finite-time stability and instability theorems in probability sense for stochastic nonlinear systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global solution.…
In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some…
We propose and study a class of numerical schemes to approximate time fractional differential equations. The methods are based on the approximation of the Caputo fractional derivative by continuous piecewise polynomials, which is strongly…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…
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…
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…