Roman Ivanovich Parovik

Roman Ivanovich Parovik
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Roman verified their affiliation via an institutional email.
Russian Academy of Sciences | RAS · Laboratory of Physical Process Modeling

DSc
Leading Researcher, Laboratory for Modeling Physical Processes, IKIR FEB RAS

About

166
Publications
17,285
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834
Citations
Additional affiliations
December 2014 - February 2024
Kamchatka State University named after Vitus Bering
Position
  • Head of Faculty
Education
September 2001 - July 2006
Kamchatka State University named after Vitus Bering
Field of study
  • Applied Mathematics and Computer Science

Publications

Publications (166)
Article
Full-text available
This article uses an approach based on the triad model–algorithm–program. The model is a nonlinear dynamic Selkov system with non-constant coefficients and fractional derivatives of the Gerasimov–Caputo type. The Adams–Bashforth–Multon numerical method from the predictor–corrector family of methods is selected as an algorithm for studying this syst...
Article
Full-text available
Using the data of radon accumulation in a chamber with excess volume at one of the points of the Kamchatka subsurface gas-monitoring network, the change in radon flux density due to seismic waves and post-seismic relaxation of the medium is shown. A linear fractional equation is considered to be a model equation. The change of radon-transport inten...
Article
Full-text available
The article is devoted to the study of economic cycles and crises, which are studied within the framework of the theory of N.D. Kondratiev long waves (K-waves). The object of the study is the fractional mathematical models of S. V. Dubovsky, consisting of two nonlinear differential equations of fractional order and describing the dynamics of the ef...
Preprint
The article uses an approach based on the triad model-algorithm-program. The model is a nonlinear dynamic Selkov system with non-constant coefficients and fractional derivatives of the Gerasimov-Caputo type. The Adams-Bashforth-Multon numerical method from the predictor-corrector family of methods is selected as an algorithm for studying this syste...
Chapter
Continuous registration of radon volume activity (RVA) is underway on the Kamchatka Peninsula and Sakhalin Island. The analysis of radon monitoring data is one of the methods for searching for earthquake precursors, since RVA is affected by changes in the stress-strain state of the geo-environment preceding seismic events. The aim of the study is t...
Chapter
The article considers program implementations of numerical algorithms for solving model equations taking into account the memory effect, adapted for execution on a computer system with parallel architecture, and also presents an analysis of parallelization efficiency. Memory (or legacy properties) are observed in many dynamic processes and mathemat...
Chapter
This chapter proposes a mathematical model built on the basis of Selkov’s nonlinear fractional dynamic system to describe the self-oscillatory modes of microseisms. Selkov’s fractional dynamical system is a system of two nonlinear ordinary differential equations with derivatives of fractional orders, understood in the Gerasimov-Caputo sense, which...
Chapter
The research of solar-terrestrial relations is of great importance both for solving practical problems and is an important problem of fundamental science. In the study, based on experimental data, the order of the fractional derivative in the previously proposed mathematical model of the dynamics of solar activity at the ascent stage is refined by...
Chapter
Geoacoustic emission is an indicator of the stress-strain state of the lithosphere, so it plays an important role in the development of methods for predicting strong earthquakes in seismically active regions such as Kamchatka. This chapter examines some aspects of the quantitative and qualitative analysis of a mathematical model of high-frequency g...
Article
Рассмотрена математическая модель образования гроз умеренных широт, учитывающая фрактальную структуру облачной среды, с применением аппарата дробного интегро-дифференцирования. В отличие от классических работ, в представленной работе процесс электризации градин в кучево-дождевых облаках умеренных широт зависит не только от напряженности электрическ...
Article
В статье исследуется динамические режимы дробной системы Селькова с переменной наследственностью (памятью). Эффект переменной наследственности означает, что наследственность изменяется во времени, т.е. зависимость текущего состояния системы от предыдущих также зависит от времени. Переменная наследственность в дробной системе Селькова с точки зрения...
Article
The paper proposes a generalization of the previously obtained mathematical model of geoacoustic emission, according to which the model takes into account the effects of heredity in dissipative terms. The model is a system of two coupled linear oscillators with non-constant coefficients and with fractional derivatives of Gerasimov-Caputo orders, wh...
Article
Full-text available
Радон — инертный радиоактивный газ, исследования вариаций которого в сопоставлении с сейсмичностью считаются перспективными для целей разработки методик прогноза землетрясений. На полуострове Камчатка развернута сеть пунктов наблюдения, в которых с помощью накопительных камер с газоразрядными счетчиками ведется мониторинг объемной активности радона...
Article
В статье предлагается принципиально новое обобщение ранее известной математической модели Зимана сердечных сокращений за счет электрохимического воздействия. Это обобщение обусловлено наличием эффектов наследственности в колебательной системе, которые указывают на то, что она может сохранять информацию о своих предыдущих состояниях. С точки зрения...
Preprint
Using data of radon accumulation in a chamber with excess volume at one of the points of the Kamchatka subsurface gas monitoring network, the change of radon flux density due to seismic waves and post-seismic relaxation of the medium is shown. Data in the temporal vicinity of a strong earthquake with Mw=7.0, which occurred in the northern part of t...
Article
Full-text available
Предложен алгоритм расчета плотности потока радона (ППР), на основе которого разработана программа («РЭКСЭМ») его расчета и визуализации одновременно с исходными данными. Программа прошла тестирования на данных, полученных сетью станций мониторинга подпочвенного радона в районе Петропавловск - Камчатского геодинамического полигона.
Article
Full-text available
Предложена модель переноса радона в пористой фрактальной среде, получены ее аналитические решения. Проведено сопоставление расчетных кривых с экспериментальными данными. Показана правомерность предположения о том, что перенос радона в грунте может осуществляться в режиме аномальной диффузии (супердиффузии).
Preprint
The article is devoted to the study of economic cycles within the framework of the theory of Kondratieff's long waves or K-waves. The object of the study is Dubovsky's fractional mathematical models, which consist of two nonlinear ordinary differential equations of fractional order and describe the dynamics of the efficiency of new technologies and...
Article
Full-text available
This research explores nonlocal problems associated with fractional diffusion equations and degenerate hyperbolic equations featuring singular coefficients in their lower-order terms. The uniqueness of the solution is established using the energy integral method, while the existence of the solution is equivalently reduced to solving Volterra integr...
Preprint
Full-text available
In this paper, we study nonlocal problems for a fractional diffusion equation and a degenerate hyperbolic equation with singular coefficients in the lower terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The existence of a solution is equivalently reduced to the question of the solvability of Volterr...
Preprint
Full-text available
The article is devoted to the research of economic cycles and crises, which are studied within the framework of the theory of long waves by N. D. Kondratiev (K-waves) using the mathematical apparatus of fractional calculus. The object of the study is the mathematical model of S.V. Dubovsky 3 and some of its modifications, which describe the dynamic...
Article
Full-text available
В работе проводится исследование дробного нелинейного осциллятора Матье методами численного анализа с целью установления его различных колебательных режимов. Дробный нелинейный осциллятор Матье представляет собой обыкновенное нелинейное дифференциальное уравнение с дробными производными в смысле Герасимова-Капуто и локальными начальными условиями (...
Article
Full-text available
В статье представлено исследование вычислительной эффективности параллельной версии численного алгоритма для решения уравнения Риккати с производной дробного перменного порядка типа Герасимова-Капуто. Численный алгоритм представляет собой нелокальную неявную конечно-разностную схему, которая сводится к системе нелинейных алгебраических уравнений и...
Book
Full-text available
The monograph outlines the main theoretical and methodological developments, which are based on an attempt to structurally generalize and systematize the basic principles of the development of national economies in general and economic systems, in particular, in describing the causes of cyclical fluctuations in the development of the latter. The th...
Chapter
The paper proposes a new mathematical model for describing the microseismic modes of interaction of two types of fractures – seed and fractures that directly generate microseisms. The mathematical model is a system of two non-linear differential equations with derivatives in the sense of Gerasimov-Caputo of fractional variable orders. The dynamical...
Article
Full-text available
В статье проводится уточнение математической модели динамики солнечной активности методом решения обратной задачи. В качестве дополнительной информации используются экспериментальные данные по наблюдению за значениями числа Вольфа. Этот параметр солнечной активности отражает число пятен на поверхности солнца, и считается индикатором его активности....
Article
Full-text available
В настоящей работе была предложена и исследована дробная динамическая система, которая описывает высокочастотную геоакустическую эмиссию с наследственностью. Модель представляет собой систему из двух связных линейных осцилляторов с непостоянными коэффициентами и производными дробного порядка Герасимова-Капуто. Каждый осциллятор описывает дислокацио...
Article
Full-text available
В работе исследуется хаотические и регулярные режимы дробной динамической системы Селькова с переменной памятью. Сначала проводится численный анализ с помощью метода Адамса-Башфорта-Мултона. Далее над полученным решением проводится предварительная обработка (модификация), которая заключается в отборе из данных значений, соответствующих локальным эк...
Article
Full-text available
A one-dimensional mathematical model of non-stationary diffusion - advection of radon in the soil - atmosphere system is considered. Using the integral Laplace transform, an analytical solution of the mathematical model was obtained and, on its basis, distribution curves of radon concentration in the soil and atmosphere were constructed. It has bee...
Article
Full-text available
В работе проведено исследование хаотических и регулярных режимов дробного осциллятора Дуффинга с помощью алгоритма Тест 0-1. Дробный осциллятор Дуффинга описывается нелинейным дифференциальным уравнением с производной Римана-Лиувилля дробного переменного порядка. С помощью явной численной конечно-разностной схемы получено численное решение модели,...
Article
Full-text available
Непрерывный мониторинг вариаций объемной активности радона с целью поиска ее аномальных значений, предшествующих сейсмическим событиям, является одной из эффективных методик исследования напряженно-деформированного состояния геосреды. Предлагается задача Коши, описывающая перенос радона с учетом его накопления в камере и наличия эффекта памяти геос...
Article
Full-text available
Citation: Gapeev, M.; Solodchuk, A.; Parovik, R. Stochastic Strike-Slip Fault as Earthquake Source Model. Mathematics 2023, 11, 3932. https:// Abstract: It is known that the source of a tectonic earthquake in the framework of the theory of elasticity and viscoelasticity is considered to be displacement along a certain fault surface. Usually, when d...
Article
Full-text available
The fractal dimension of geomagnetic field component variations (horizontal—H, vertical—Z and magnetic declination—D) at the Baigazan magnetic station at Russian Altay, for the period 2011–2013, were calculated using the Higuchi method. The daily variation of Higuchi Fractal Dimension (HFD) for the D, H, Z components of the geomagnetic field were i...
Preprint
Full-text available
It is known that the source of a tectonic earthquake in the framework of the theory of elasticity and viscoelasticity is considered as a displacement along a certain fault surface. Usually, when describing the source, the geometry of the fault surface is simplified to a flat rectangular area. The displacement vector is assumed to be constant. In th...
Article
Full-text available
The numerical solution for fractional dynamics problems can create a high computational load, which makes it necessary to implement efficient algorithms for their solution. The main contribution to the computational load of such computations is created by heredity (memory), which is determined by the dependence of the current value of the solution...
Article
Full-text available
The article presents a software implementation of a parallel efficient and fast computational algorithm for solving the Cauchy problem for a nonlinear differential equation of a fractional variable order. The computational algorithm is based on a non-local explicit finite-difference scheme, taking into account the approximation of the Gerasimov-Cap...
Preprint
Full-text available
The fractal dimension of geomagnetic variations at the Baigazan magnetic station at Russian Altay for 2011-2013 was calculated using the Higuchi method. The daily variation of Higuchi Fractal Dimension (HFD) for the D,H,Z-components of the geomagnetic field has been investigated, its contribution to the variability of HFD is from 30 to 40 percent o...
Article
Full-text available
В статье предложено обобщение математической модели Макшерри для моделирования искусственной электрокардиограммы — изменяющегося во времени сигнала, отражающий ионный ток, который заставляет сердечные волокна сокращаться, а затем расслабляться. Обобщение математической модели Макшерри заключается в учете свойства наследственности (памяти) динамичес...
Article
Full-text available
Геоакустическая эмиссия является индикатором напряженно-деформированного состояния геосферы, поэтому она играет важную роль в разработке методики прогнозирования сильных землетрясений в сейсмоактивных регионах, таких как Камчатка. В работе исследуются некоторые аспекты качественного анализа математической модели высокочастотной геоакустической эмис...
Book
Full-text available
With the help of fractional calculus, the non-linear Duffing oscillator, which occurs in various problems of physics, biology, economics and other sciences, is studied. For quantitative analysis, nonlocal explicit and non-local finite-difference schemes, the issues of stability and convergence are investigated, approbation is carried out on test ex...
Article
Full-text available
Mathematical modeling is used to study the hereditary mechanism of the accumulation of radioactive radon gas in a chamber with gas-discharge counters at several observation points in Kamchatka. Continuous monitoring of variations in radon volumetric activity in order to identify anomalies in its values is one of the effective methods for studying t...
Article
Full-text available
The article considers an implicit finite-difference scheme for the Duffing equation with a derivative of a fractional variable order of the Riemann–Liouville type. The issues of stability and convergence of an implicit finite-difference scheme are considered. Test examples are given to substantiate the theoretical results. Using the Runge rule, the...
Article
Full-text available
В этой статье проводится математическое моделирование динамики солнечной активности. Исследуются данные наблюдений по средне-ежемесячному числу солнечных пятен, называемых числом Вольфа, в период за 24.5 года с мая 1996 года по октябрь 2022 года. Исходя из результатов подобного исследования данных по этому процессу, с применением уравнения Риккати...
Article
Full-text available
Предложена дробная нелинейная динамическая система Селькова, для описания микросейсмических явлений. Эта система известна наличием автоколебательных режимов и применяется в биологии для описания гликолитических колебаний субстрата и продукта. Динамическая система Селькова также может по аналогии описать взаимодействие двух видов трещин в упруго-хру...
Article
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В статье проводится математическое моделирование электромагнитной динамики атмосферика. Атмосферик – широкополосный сигнал с максимумом интенсивности в диапазоне частот 8-10 кГц, который распространяется в виде плоской электромагнитной волны в сложной структуре проводящего пространства волновода, образованного поверхностью Земли и ионосферой. Матем...
Article
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Статья посвящена построению математической модели высокочастотной (от единиц до десятков килогерц) геоакустической эмиссии приповерхностных осадочных пород, регистрируемой на Камчатке. В основе модели лежит система связанных осцилляторов. Каждый осциллятор описывает дислокационный источник геоакустической эмиссии. Модель строится на основании предп...
Article
Full-text available
На Петропавловск-Камчатском геодинамическом полигоне работает сеть пунктов мониторинга подпочвенных газов. За время работы сети в поле подпочвенных газов были зарегистрированы аномалии, предваряющие сильные землетрясения с магнитудой М>5. По морфологическим признакам они разделены на два типа А и Б. В работе описывается разработанное программное об...
Article
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В статье рассматривается неявная конечно-разностная схема для уравнения Дуффинга с производной дробного переменного порядка типа Римана-Лиувилля. Рассматриваются вопросы устойчивости и сходимости неявной конечно-разностной схемы. Для обоснования теоретических результатов приводятся тестовые примеры. С помощью правила Рунге сравниваются результаты р...
Article
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В этой статье была использована дробно-дифференциальная модель физических процессов с насыщением для описания динамики летальных исходов инфекции COVID-19. Математическое описание модели дается интегро-дифференциальным уравнением Риккати с производной дробного переменного порядка типа Герасимова-Капуто. Такое описание позволяет учитывать эффекты на...
Article
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The paper considers algorithms for constructing maps of dynamic regimes and bifurcation diagrams in nonlinear dynamics using the example of some oscillatory systems and discrete mappings. The work is educational and methodical and can be used in the educational process when studying the disciplines “Nonlinear dynamics” and “Theory of oscillatory sy...
Article
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A non-linear fractional Selkov dynamic system for mathematical modeling of microseismic phenomena is proposed. This system is a generalization of the previously known Selkov system, which has self-oscillatory modes and is used in biology to describe glycolytic vibrations of the substrate and product. The Selkov fractional dynamical system takes int...
Article
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During the eruption of the Kizimen volcano in 2010-2013 there was a uniform squeezing of the viscous lava flow. Simultaneously with its movement, earthquakes with an unusual quasi-periodicity were recorded, the "drumbeats" mode. In this work, we show that these earthquakes were generated by the movement of the flow front, which was observed for the...
Conference Paper
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The article proposes a computer program for calculating economic crises according to the generalized mathematical model of S.V. Dubovsky. This model is represented by a system of ordinary nonlinear differential equations with fractional derivatives in the sense of Gerasimov-Caputo with initial conditions. Furthermore, according to a numerical algor...
Conference Paper
Full-text available
In this paper, we consider some aspects of the numerical analysis of the mathematical model of fractional Duffing with a derivative of variable fractional order of the Riemann-Liouville type. Using numerical methods: an explicit finite-difference scheme based on the Grunwald-Letnikov and Adams-Bashford-Moulton approximations (predictor-corrector),...
Article
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The paper is devoted to derivation of the optimal interpolation formula in W2(0,2)(0,1) Hilbert space by Sobolev’s method. Here the interpolation formula consists of a linear combination ΣNβ=0Cβφ(xβ) of the given values of a function φ from the space W2(0,2)(0,1). The difference between functions and the interpolation formula is considered as a lin...
Article
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In this paper, a numerical analysis of the oscillation equation with a derivative of a fractional variable Riemann–Liouville order in the dissipative term, which is responsible for viscous friction, is carried out. Using the theory of finite-difference schemes, an explicit finite-difference scheme (Euler’s method) was constructed on a uniform compu...
Article
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In this study, the model Riccati equation with variable coefficients as functions, as well as a derivative of a fractional variable order (VO) of the Gerasimov-Caputo type, is used to approximate the data for some physical processes with saturation. In particular, the proposed model is applied to the description of solar activity (SA), namely the n...
Book
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The monograph is devoted to some aspects of the study of chaotic and regular regimes of fractional oscillators. Using numerical methods, an algorithm for calculating the spectra of maximum Lyapunov exponents for determining the chaotic dynamics of nonlinear fractional oscillators has been developed. A numerical algorithm has been developed for calc...
Book
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Complex methods and results of studies of physical processes and their interactions in the system of near space and geospheres under conditions of increased variability of solar, cyclonic and seismic activity are presented. The results of long-term observations are summed up. Methods of system analysis have been developed. Models of nonlinear and r...
Book
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The monograph is devoted to the study of dynamic processes with saturation and memory using the fractional Riccati equation. Numerical methods for solving using non-local explicit and implicit finite-difference schemes are proposed, questions of stability and convergence of methods are investigated, test calculations are carried out, and computer p...
Article
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The results of modeling the conversion factor from rainfall-deposited unit activity of gamma-emitting radon and thoron daughter decay products to their created gamma-radiation dose rate as a function of height above the Earth’s surface using the Geant4 toolkit are presented in this paper. Thin layers of water, soil, and air, with the height of 0.1–...
Article
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The article discusses different schemes for the numerical solution of the fractional Riccati equation with variable coefficients and variable memory, where the fractional derivative is understood in the sense of Gerasimov-Caputo. For a nonlinear fractional equation, in the general case, theorems of approximation, stability, and convergence of a non...
Article
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Работа посвящена исследованию гамма-фона в городской среде Петропавловска-Камчатского (Камчатский край), а именно в парках и зонах отдыха. Измерения мощности поглощенной дозы проводились на разработанном коллективном Томского политехнического университета (ТПУ) дозиметре с использованием органического сцинтиллятора ВС-408, который является схожим п...
Article
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The paper investigates the dynamic modes of the Sel’kov fractional self-oscillating system in order to simulate the interaction of cracks. The spectra of the maximum Lyapunov exponents, constructed depending on the parameters of the dynamic system, are used as a research tool. The maximum Lyapunov exponents were constructed according to the Benetti...
Article
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The article proposes a mathematical model based on the fractional Riccati equation to describe the dynamics of COVID-19 coronavirus infection in the Republic of Uzbekistan and the Russian Federation. The model fractional Riccati equation is an equation with variable coefficients and a derivative of a fractional variable order of the Gerasimov-Caput...
Article
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The features of the atmospheric γ-background reaction to liquid atmospheric precipitation in the form of bursts is investigated, and various forms of them are analyzed. A method is described for interpreting forms of the measured γ-background response with the determination of the beginning and ending time of precipitation, the distinctive features...
Article
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The article proposes a nonlocal explicit finite-difference scheme for the numerical solution of a nonlinear, ordinary differential equation with a derivative of a fractional variable order of the Gerasimov–Caputo type. The questions of approximation, convergence, and stability of this scheme are studied. It is shown that the nonlocal finite-differe...
Conference Paper
Full-text available
In this paper, we study the Cauchy problem for the Riccati differential equation with constant coefficients and a modified Gerasimov-Caputo type fractional differential operator of variable order. Using Newton’s numerical algorithm, calculation curves are constructed taking into account different values of the Cauchy problem parameters. The calcula...
Conference Paper
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In this paper, we study the conditions of global solvability and unsolvability in time of solutions to the nonlinear diffusion problem based on self-similar analysis. We constructed various self-similar solutions of the nonlinear diffusion problem in the slow diffusion case. We established critical exponents of the Fujita type and critical exponent...
Conference Paper
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The paper presents a numerical analysis of the class of mathematical models of linear fractional oscillators, which is the Cauchy problem for a differential equation with derivatives of fractional orders in the sense of Gerasimov-Caputo. A method based on an explicit nonlocal finite-difference scheme (ENFDS) and the Adams-Bashfort-Moulton (ABM) met...
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The paper proposes a new mathematical model of economic cycles and crises, which generalizes the well-known model of Dubovsky S.V. The novelty of the proposed model lies in taking into account the effect of heredity (memory), as well as the introduction of harmonic functions responsible for the arrival of investments in fixed assets and new managem...
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With regard to reconstructing the gamma background dose rate, existing models are either empirical with limited applicability or have many unknown input parameters, which complicates their application in practice. Due to this, there is a need to search for a new approach and build a convenient, easily applicable and universal model. The paper propo...
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During the eruption of the Kizimen volcano in 2010-2013. There was a uniform squeezing of the viscous lava flow. Simultaneously with its movement, earthquakes with an unusual quasi-periodicity were recorded, the "drumbeats" mode. In this work, we show that these earthquakes were generated by the movement of the flow front, which was observed for th...
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In this paper, we consider some aspects of the numerical analysis of the mathematical model of fractional Duffing with a derivative of variable fractional order of the Riemann-Liouville type. Using numerical methods: an explicit finite-difference scheme based on the Grunwald-Letnikov and Adams-Bashford-Moulton approximations (predictor-corrector),...
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Results and prospects of work of the integrative laboratory "Natural disasters of Kamchatka - earthquakes and volcanic eruptions".
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The eruption of the Kizimen volcano in 2011-2012 characterized by stable, almost uniform squeezing of a viscous lava flow with a volume of 0.3 km3. The formation of the lava flow was accompanied by the occurrence of quasiperiodic earthquakes of the “drumbeats” mode with energy classes Ks < 7, recorded at long time intervals. Shown that earthquakes...
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The article proposes a computer program for calculating economic crises according to the generalized mathematical model of S.V. Dubovsky. This model is represented by a system of ordinary nonlinear differential equations with fractional derivatives in the sense of Gerasimov-Caputo with initial conditions. Furthermore, according to a numerical algor...
Preprint
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The paper proposes a new mathematical model of economic cycles and crises, which generalizes the well-known model of Dubovsky S.V. The novelty of the proposed model lies in taking into account the effect of heredity (memory), as well as the introduction of harmonic functions responsible for the arrival of investments in fixed assets and new managem...
Preprint
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In this paper, we study the Cauchy problem for the Riccati differential equation with constant coefficients and a modified Gerasimov-Caputo type fractional differential operator of variable order. Using Newton's numerical algorithm, calculation curves are constructed taking into account different values of the Cauchy problem parameters. The calcula...
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The paper presents a numerical analysis of the class of mathematical models of linear fractional oscillators, which is the Cauchy problem for a differential equation with derivatives of fractional orders in the sense of Gerasimov-Caputo. A method based on an explicit nonlocal finite-difference scheme (ENFDS) and the Adams-Bashfort-Moulton (ABM) met...
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In this paper we suggest an explicit finite-difference scheme for numerical simulation of the Cauchy problem with an integro-differential nonlinear equation that describes an oscillatory process with friction and memory (hereditarity), and with the corresponding local initial conditions. The problems of approximation, stability, and convergence of...
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The article proposes a mathematical model of radon accumulation in a chamber, which takes into account the hereditary properties of the environment in which radon migrates. The model equation is the fractional Riccati equation with a derivative of a fractional variable order of the Gerasimov-Caputo type, taking into account heredity, as well as tak...
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The paper presents a mathematical model of radon accumulation in a chamber, which takes into account the hereditary properties of the environment in which radon migrates, and also uses a nonlinear function that is responsible for the mechanisms of radon entering the chamber. The simulation of accumulation is performed in comparison with real data....
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Microseismic phenomena are studied by a Sel'kov generalized nonlinear dynamic system. This system is mainly applied in biology to describe substrate and product glycolytic oscillations. Thus, Sel'kov dynamic system can also describe interaction of two types of fractures in an elastic-friable medium. The first type includes seed fractures with lower...
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The article investigates a mathematical model of the Duffing oscillator with a variable fractional order derivative of the Riemann-Liouville type. The study of the model is carried out using a numerical scheme based on the approximation of the fractional derivative of the Riemann-Liouville type by a discrete analog-the fractional derivative of Grun...
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In the present paper the problem of construction of optimal quadrature formulas in the sense of Sard in the space L2(m)(0,1) is considered. Here the quadrature sum consists of values of the integrand at nodes and values of the first and the third derivatives of the integrand at the end points of the integration interval. The coefficients of optimal...
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In this work, based on Newton's second law, taking into account heredity, an equation is derived for a linear hereditary oscillator (LHO). Then, by choosing a power-law memory function, the transition to a model equation with Gerasimov-Caputo fractional derivatives is carried out. For the resulting model equation, local initial conditions are set (...
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A non-linear fractional oscillator is a generalization of a classical non-linear oscillator in consideration of the hereditary or the memory effect. The memory effect is a property of a dynamic system in which its current state depends on a finite number of its previous states. Therefore, a non-linear fractional oscillator can be mathematically des...