Stability theory for some scalar finite difference schemes: validity of the modified equations approach* [PDF]
ESAIM: Proceedings and Surveys, 2021 In this paper, we discuss some limitations of the modified equations approach as a tool for stability analysis for a class of explicit linear schemes to scalar partial differential equations. We show that the infinite series obtained by Fourier transform
Dhaouadi Firas +3 more
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Stability and boundedness In nonlinear and neutral difference equations using new variation of parameters formula and fixed point theory [PDF]
Cubo, 2019 In the case of nonlinear problems, whether in differential or difference equations, it is difficult and in some cases impossible to invert the problem and obtain a suitable mapping that can be effectively used in fixed point theory to qualitatively ...
Youssef N. Raffoul
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Study of the stability of a 3×3 system of difference equations using Centre Manifold Theory.
Appl. Math. Lett., 2017 Nikolaos Psarros +2 more
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Stability Analysis for a Class of Stochastic Differential Equations with Impulses
Mathematics, 2023 This paper is concerned with the problem of asymptotic stability for a class of stochastic differential equations with impulsive effects. A sufficient criterion on asymptotic stability is derived for such impulsive stochastic differential equations via ...
Mingli Xia +3 more
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Riccati equations in stability theory of difference equations with memory [PDF]
1999 European Control Conference (ECC), 1999 This paper defines several Riccati equations that allow checking the stability of difference equations with delay effect as x i+1 = mΣ j=0 A j x i-j (x i ∊ Rn). These various matrix Riccati equations have the same dimension n than the vector x, whatever the order m may be: this represents an advantage for high orders m when compared to classical ...
Vladimir Kolmanovskii +2 more
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On a functional equation arising in the stability theory of difference-differential equations [PDF]
Quarterly of Applied Mathematics, 1977 The functional differential equation \[ Q ′
Castelan, W. B., Infante, E. F.
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Nonlocal Problems for Hilfer Fractional q-Difference Equations
Fractal and Fractional, 2023 In the paper, we investigate a kind of Hilfer fractional q-difference equations with nonlocal condition. Firstly, the existence and uniqueness results of solutions are obtained by using topological degree theory and Banach fixed point theorem ...
Chunping Tian, Haibo Gu, Zunkai Yang
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Some Unsolved Problems in Stability and Optimal Control Theory of Stochastic Systems
Mathematics, 2022 In spite of the fact that the theory of stability and optimal control for different types of stochastic systems is well developed and very popular in research, there are some simply and clearly formulated problems, solutions of which have not been found ...
Leonid Shaikhet
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Stability theory and adjoint operators for linear differential-difference equations [PDF]
Transactions of the American Mathematical Society, 1959 Abstract : This paper extends to linear differential-difference equations a number of results familiar in the stability theory of ordinary linear differential equations. In this theory, one considers a system of equations of the form (1) dx/dt = A(t)x, x(0) = c, where t is a real variable, x is a column vector with n rows, and A(t) is an n- by -n ...
Bellman, Richard, Cooke, Kenneth L.
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Journal of Low Frequency Noise, Vibration and Active Control, 2021 A new dynamical model with five rigid frames (RFs), driven by two counter-rotating exciters, is proposed to explore the synchronization, stability, and motion characteristics of the system in this paper.
Wenchao Hu +4 more
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