Asymptotic stability of solutions to Volterra-renewal integral equations with space maps

Annunziato, Mario; Brunner, Hermann; Messina, Eleonora

doi:10.1016/j.jmaa.2012.05.080

Cited by 11 publications

(10 citation statements)

References 20 publications

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“…In addition, it is known that for quite broad classes of MT the use of IDM and, in particular, the models of equivalent DE, makes it possible to receive the basis for building highly stable numerical algorithms for analysis and calculation of their parameters [8,20,21].…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Development of the method for creating explicit integral dynamic models of measuring transducers

Sytnik

Protasov

Klyuchka

2017

EEJET

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Розглянутий в статті метод полягає у визначен-ні імпульсної перехідної характеристики за заданими диференціальними рівняннями, яка є ядром явної інте-гральної динамічної моделі вимірювальних перетво-рювачів, як з розподіленими, так і з зосередженими параметрами. Інтегральні динамічні моделі дозволя-ють розширити алгоритмічні основи комп'ютерного моделювання у задачах дослідження вимірювальних перетворювачів та надають досліднику можливість вибору оптимального виду математичної моделі Ключові слова: інтегральна динамічна модель, імпульсна перехідна функція, вимірювальний пере-творювач, диференціальне рівняння Рассмотренный в статье метод заключается в определении импульсной переходной характеристи-ки по заданным дифференциальным уравнениям, которая является ядром явной интегральной дина-мической модели измерительных преобразователей, как с распределенными, так и с сосредоточенны-ми параметрами. Интегральные динамические моде-ли позволяют расширить алгоритмические основы компьютерного моделирования в задачах исследо-вания измерительных преобразователей, а также предоставляют исследователю возможность выбора оптимального вида математической модели Ключевые слова: интегральная динамическая модель, импульсная переходная функция, измеритель-ный преобразователь, дифференциальное уравнение UDC 681. 51

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

Development of the method for creating explicit integral dynamic models of measuring transducers

Sytnik

Protasov

Klyuchka

2017

EEJET

View full text Add to dashboard Cite

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“…This equation can be discretized as in [6,4], and then solved numerically. Briefly, let Π M := {x 1 , .…”

Section: A Practical Application Examplementioning

confidence: 99%

“…The normalized kernel scheme [4] guarantees the asymptotic convergence of the numerical method. After which the discrete distribution functions can be evaluated by the discrete version of the points 7-11 of the Summary.…”

Section: A Practical Application Examplementioning

confidence: 99%

On the Action of a Semi-Markov Process on a System of Differential Equations

Annunziato

2012

Mathematical Modelling and Analysis

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We deal with a model equation for stochastic processes that results from the action of a semi-Markov process on a system of ordinary differential equations. The resulting stochastic process is deterministic in pieces, with random changes of the motion at random time epochs. By using classical methods of probability calculus, we first build and discuss the fundamental equation for the statistical analysis, i.e. a Liouville Master Equation for the distribution functions, that is a system of hyperbolic PDE with non-local boundary conditions. Then, as the main contribute to this paper, by using the characteristics' method we recast it to a system of Volterra integral equations with space fluxes, and prove existence and uniqueness of the solution. A numerical experiment for a case of practical application is performed.

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“…More recently, classes of more significative linear convolution equations (see, for example [2] and [21]) have been considered as test equations for numerical purposes, whereas the stability theory on nonlinear problems is much less developed and much more tuned to the characteristics of the problem itself [11,13,22,23]. It turns out that, for the specific equation 1, the numerical stability theory on nonlinear problems developed in recent years do not apply and, furthermore, classical stability results on linearized equations may not take into account important changes in the behavior of the solution.…”

mentioning

confidence: 99%

“…We are now in the position to prove the following theorem, which is the discrete equivalent of Theorem 3 in [26]. For the proof we closely refer to [2] and [12].…”

mentioning

confidence: 99%

Numerical simulation of a SIS epidemic model based on a nonlinear Volterra integral equation

Messina¹

2015

Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madr

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We consider a SIS epidemic model based on a Volterra integral equation and we compare the dynamical behavior of the analytical solution and its numerical approximation obtained by direct quadrature methods. We prove that, under suitable assumptions, the numerical scheme preserves the qualitative properties of the continuous equation and we show that, as the stepsize tends to zero, the numerical bifurcation points tend to the continuous ones

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Asymptotic stability of solutions to Volterra-renewal integral equations with space maps

Cited by 11 publications

References 20 publications

Development of the method for creating explicit integral dynamic models of measuring transducers

Development of the method for creating explicit integral dynamic models of measuring transducers

On the Action of a Semi-Markov Process on a System of Differential Equations

Numerical simulation of a SIS epidemic model based on a nonlinear Volterra integral equation

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