Solution estimates and stability tests for linear neutral differential equations

Berezansky, Leonid; Braverman, Elena

doi:10.1016/j.aml.2020.106515

Cited by 6 publications

(7 citation statements)

References 11 publications

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“…in the scalar case. In the present paper we extend the results obtained in [4] to a system ẋ(t) − A(t) ẋ(g(t)) = m k=1 B k (t)x(h k (t)), t ≥ t 0 ≥ 0, (1.2) where some of the stability tests are new also for scalar equation (1.1) (we will discuss this question in the last section) and for a vector linear delay differential equations without the neutral part when A(t) ≡ 0.…”

Section: Introductionsupporting

confidence: 88%

“…There are many papers and monographs on stability of scalar neutral differential equations, see a review of explicit stability tests for this class of equations in [3,4]. For linear vector neutral delay equations, explicit exponential stability results can be found in the monographs [1,11,13,19,20,27] and the papers [2,9,12,15,17,23,24,25,26].…”

Section: Introductionmentioning

confidence: 99%

“…LMI (linear matrix inequality) method is also based on the method of Lyapunov-Krasovskii functionals [10,22,26]. Some stability results were obtained by using the Bohl-Perron theorem [1,3,4,5,6,7,9] and application of special properties of matrices, including fundamental matrix functions for differential equations [11,14,15,24,25]. Several tests for linear and nonlinear scalar neutral equations were obtained by the fixed point method [18,30].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Asymptotic properties of neutral type linear systems

Berezansky¹,

Braverman²

2020

Preprint

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Exponential stability and solution estimates are investigated for a delay systemof a neutral type, where A and B k are n × n bounded matrix functions, and g, h k are delayed arguments. Stability tests are applicable to a wide class of linear neutral systems with time-varying coefficients and delays. In addition, explicit exponential estimates for solutions of both homogeneous and non-homogeneous neutral systems are obtained for the first time. These inequalities are not just asymptotic estimates, they are valid on every finite segment and evaluate both short-and long-term behaviour of solutions.

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Section: Introductionsupporting

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic properties of neutral type linear systems

Berezansky¹,

Braverman²

2020

Preprint

Self Cite

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“…There are many numerical optimization algorithms in the literature that can be used to solve (3). Classical techniques use the gradient of the cost function J in (4) to estimate the minimizer.…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation in Neutral Delay Differential Equations Using Genetic Algorithm With Multi-Parent Crossover

Jamilla

Mendoza

2021

IEEE Access

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Neutral delay differential equations (NDDEs) are differential equations containing time lags not only in the states but also in the state derivatives. NDDEs have applications in modeling physical and biological systems. An NDDE model may consist of several parameters, some of which can be determined using available data. Various numerical techniques have been studied to estimate parameters of mathematical models. In this study, parameter estimation is posed as an optimization problem. The use of heuristic algorithms in parameter estimation has gained popularity because of its ease of implementation, requiring only function evaluations. But to our knowledge, heuristic algorithms have never been employed in estimating parameters in NDDE models. In this work, we apply Genetic Algorithm with Multi-Parent Crossover (GA-MPC) to obtain parameter estimates of three NDDE models with a discrete delay. We compare the estimates to those obtained using standard heuristic algorithms. Results show that GA-MPC is capable of consistently identifying model parameters that provide a good fit of the model to the data.INDEX TERMS neutral delay differential equations, parameter estimation, genetic algorithm, bootstrapping, inverse problem, heuristic algorithms VOLUME x, 20xx

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“…Heat transfer is one of the physical phenomena which described the Laplace or Poisson partial differential equation (Mortazavi & Moghaddam, 2016;Idesman & Dey, 2020;Conte, 2020;Berezansky & Braverman, 2020). Heat transfer is a concept for predicting energy transfer due to the temperature differences between two positions or materials, which can be observed by the direction of moving particles or by the effects (Liu, Wang, & Yi, 2020;Karami & Kamkari, 2020;Zhang, Gao, & Huang, 2017).…”

Section: Introductionmentioning

confidence: 99%

Heat Flow Transport Model by Gauss-Seidel Type Iteration Methods for Gas and Solid Materials

Rauf¹,

Haeruddin

Rahmat³

et al. 2021

JFF

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Technological processes for modification of materials, deposition, and prevented fumes in the pyrolysis processes are used gases materials in the medium with vacuum pressure or atmospheric air pressure. Therefore, it is essential to understand heat flow transport for designing an eﬃcient reactor or find the substrate's excellent position in the reactor or furnace for growing materials. We evaluated the energy transfer phenomena in the form of temperature distribution and heat flow for various heating sources for the gases and solid materials by Gauss-Seidel equation. The thermal conductivity coefficient (k), number of heating sources, and position of heating sources show an essential parameter for transmitting the distribution of the heat. For high k value shows efficiently for heat transfer at low temperature due to the atom's position close each other. The heat also affects to the phonon and lattice vibration like a wave which successfully shows these phenomena in this study.

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Solution estimates and stability tests for linear neutral differential equations

Cited by 6 publications

References 11 publications

Asymptotic properties of neutral type linear systems

Asymptotic properties of neutral type linear systems

Parameter Estimation in Neutral Delay Differential Equations Using Genetic Algorithm With Multi-Parent Crossover

Heat Flow Transport Model by Gauss-Seidel Type Iteration Methods for Gas and Solid Materials

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