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Three Results on the Nonlinear Differential Equations and Differential-Difference Equations
Mathematics, 2019 We mainly study the transcendental entire solutions of the differential equation f n ( z ) + P ( f ) = p 1 e α 1 z + p 2 e α 2 z , where p 1 , p 2 , α 1 and α 2 are nonzero
Jianxun Rong, Junfeng Xu
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IEEE Access, 2021 This paper considers exponential stability for a class of timescale-type differential-difference equation with bounded time-varying delay. Based on time scale theory, internally positive representation technique, as well as the existing exponential ...
Qiang Xiao, Yin Yang, Tingwen Huang
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APPROXIMATION OF SOLUTIONS OF A DIFFERENCE-DIFFERENTIAL EQUATION [PDF]
, 1977 summary:In the present paper we study the approximate solutions of a certain difference-differential equation under the given initial conditions. The well known Gronwall-Bellman integral inequality is used to establish the results.
Pachpatte, B. G. +2 more
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Solutions of the neutral differential-difference equation αx′(t)+βx′(t−r)+γx(t)+δx(t−r)=f(t)
International Journal of Mathematics and Mathematical Sciences, 1992 Particular solutions and complementary functions are obtained for the functional equation αx′(t)+βx′(t−r)+γx(t)+δx(t−r)=f(t) in the forms of a convolution type integral and of infinite series.
Ll. G. Chambers
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Nonlocal Tricomi boundary value problem for a mixed-type differential-difference equation [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2021 We investigate the Tricomi boundary value problem for a differential-difference leading-lagging equation of mixed type with non-Carleman deviations in all in all arguments of the required function.
Alexandr Nikolaevich Zarubin
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Stability for Differential Difference Equations
Journal of Mathematical Analysis and Applications, 1993 The authors consider the retarded differential difference equation \(\dot x(t)=A_ 0 x(t)+\sum^ N_{k=1} A_ k x(t-\gamma_ k\cdot r)\) and the neutral differential difference equation \[ {d\over {dt}} \left[ x(t)- \sum^ N_{k=1} B_ k x(t-\gamma_ k\cdot r)\right] =A_ 0 x(t)+ \sum^ N_{k=1} A_ k x(t-\gamma_ k\cdot r), \] where \(x\in\mathbb{R}^ n\), each \(A_
Liao, X.X., Wang, X.J.
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Characteristics of Conservation Laws for Difference Equations [PDF]
, 2013 Each conservation law of a given partial differential equation is determined (up to equivalence) by a function known as the characteristic. This function is used to find conservation laws, to prove equivalence between conservation laws, and to prove the ...
Hydon, PE +3 more
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Poisson Λ-brackets for Differential–Difference Equations [PDF]
International Mathematics Research Notices, 2018 Abstract We introduce the notion of a multiplicative Poisson $\lambda$-bracket, which plays the same role in the theory of Hamiltonian differential–difference equations as the usual Poisson $\lambda$-bracket plays in the theory of Hamiltonian partial differential equations (PDE).
De Sole A. +3 more
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Polynomial solutions of differential–difference equations
Journal of Approximation Theory, 2011 We investigate the zeros of polynomial solutions to the differential-difference equation \[ P_{n+1}(x)=A_{n}(x)P_{n}^{\prime}(x)+B_{n}(x)P_{n}(x), n=0,1,... \] where $A_{n}$ and $B_{n}$ are polynomials of degree at most 2 and 1 respectively. We address the question of when the zeros are real and simple and whether the zeros of polynomials of adjacent ...
Diego Dominici +2 more
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Improving Particle Swarm Optimization Analysis Using Differential Models
Applied Sciences, 2022 This paper employs the approach of the differential model to effectively improve the analysis of particle swarm optimization. This research uses a unified model to analyze four typical particle swarm optimization (PSO) algorithms.
Sung-Jung Hsiao, Wen-Tsai Sung
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