/ A. I. Levykin, E. A. Novikov // Doklady Mathematics. - 1996. - Vol. 53, Is. 3. - P377-380
. - ISSN 1064-5624
Scopus
Держатели документа:
Computing Center, Siberian Division, Russian Academy of Sciences, pr. Lavrent'eva 6, Novosibirsk, 630090, Russian Federation
Computing Center, Siberian Division, Russian Academy of Sciences, Akademgorodok, Krasnoyarsk, 660036, Russian Federation
ИВМ СО РАН
Доп.точки доступа:
Levykin, A.I.; Novikov, E.A.; Новиков, Евгений Александрович
Труды сотрудников ИВМ СО РАН
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Найдено документов в текущей БД: 6
The class of (m, k)-methods for solving implicit systems of ODE
[Текст] / A. I. Levykin, E. A. Novikov // Dokl. Akad. Nauk. - 1996. - Vol. 348, Is. 4. - С. 442-445. - Cited References: 12
. - ISSN 0869-5652
РУБ Multidisciplinary Sciences
WOS
Держатели документа:
RUSSIAN ACAD SCI,CTR COMP,KRASNOYARSK,RUSSIA
ИВМ СО РАН
Доп.точки доступа:
Levykin, A.I.; Лепихин, Анатолий Михайлович; Novikov, E.A.; Новиков, Евгений Александрович
WOS
Держатели документа:
RUSSIAN ACAD SCI,CTR COMP,KRASNOYARSK,RUSSIA
ИВМ СО РАН
Доп.точки доступа:
Levykin, A.I.; Лепихин, Анатолий Михайлович; Novikov, E.A.; Новиков, Евгений Александрович
A Study of (m,k)-methods for solving differential-algebraic systems of index 1
/ A. I. Levykin, E. A. Novikov // Communications in Computer and Information Science . - 2015. - Vol. 549: 8th International Conference on Mathematical Modeling of Technological Processes, CITech 2015; Almaty; Kazakhstan; 24 September 2015 through 27 September 2015; Code 159049. - P94-107, DOI 10.1007/978-3-319-25058-8_10
. -
Кл.слова (ненормированные):
Differential-algebraic systems of index 1 -- Numerical methods -- Stiff systems -- Differential equations -- Initial value problems -- Numerical methods -- Ordinary differential equations -- Differential algebraic systems -- Implicit systems -- Numerical solution -- Order conditions -- Schemes optimal -- Stiff systems -- Algebra
Аннотация: A class (m,k)-methods is discussed for the numerical solution of the initial value problems for implicit systems of ordinary differential equations. The order conditions and convergence of the numerical solution in the case of implementation of the scheme with the time-lagging of matrices derivatives for systems of index 1 are obtained. At k ? 4 the order conditions are studied and schemes optimal computing costs are obtained. © Springer International Publishing Switzerland 2015.
Scopus
Держатели документа:
Institute of Computational Mathematics and Mathematical Geophysics, Academy of Sciences, Siberian Branch, pr. Ak. Lavrent’eva 6, Akademgorodok, Novosibirsk, Russian Federation
Institute of Computational Modeling, Academy of Sciences, Siberian Branch, Akademgorodok 50, Str. 4, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Novikov, E. A.; Новиков, Евгений Александрович
Кл.слова (ненормированные):
Differential-algebraic systems of index 1 -- Numerical methods -- Stiff systems -- Differential equations -- Initial value problems -- Numerical methods -- Ordinary differential equations -- Differential algebraic systems -- Implicit systems -- Numerical solution -- Order conditions -- Schemes optimal -- Stiff systems -- Algebra
Аннотация: A class (m,k)-methods is discussed for the numerical solution of the initial value problems for implicit systems of ordinary differential equations. The order conditions and convergence of the numerical solution in the case of implementation of the scheme with the time-lagging of matrices derivatives for systems of index 1 are obtained. At k ? 4 the order conditions are studied and schemes optimal computing costs are obtained. © Springer International Publishing Switzerland 2015.
Scopus
Держатели документа:
Institute of Computational Mathematics and Mathematical Geophysics, Academy of Sciences, Siberian Branch, pr. Ak. Lavrent’eva 6, Akademgorodok, Novosibirsk, Russian Federation
Institute of Computational Modeling, Academy of Sciences, Siberian Branch, Akademgorodok 50, Str. 4, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Novikov, E. A.; Новиков, Евгений Александрович
Numerical Simulation of Chemical Kinetics With a Two-Stage Method for Solving Implicit Systems
[Text] : статья / A. E. Novikov, E. A. Novikov, A. I. Levykin // Университетский научный журнал. - 2017. - № 30. - P21-29
. - ISSN 2222-5064
Перевод заглавия: Численное моделирование химической кинетики двухстадийным методом решения неявных систем
Кл.слова (ненормированные):
Неявная система -- метод Розенброка -- контроль точности -- Implicit system -- Rosenbrock method -- accuracy control
Аннотация: The Cauchy problem for a stiff system of ODEs unresolved with respect to the derivative often arises in chemical kinetics, mechanical engineering, and other important applications. The two-stage L-stable Rosenbrock-type method is derived. An integration algorithm of alternating stepsize is designed based on the method, aimed at solving implicit stiff systems of ODEs. Numerical results confirming the efficiency of the new algorithm are given.
В химической кинетике, машиностроении и в других важных приложениях возникает задача Коши для жесткой системы ОДУ неразрешенных относительно производной. Построен двухстадийный L-устойчивый метод типа Розенброка, предназначенный для решения неявных жестких систем ОДУ. На основе этого метода сформулирован алгоритм интегрирования переменного шага. Приведены результаты расчетов, подтверждающие эффективность нового алгоритма.
РИНЦ
Держатели документа:
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Institute of computational modeling SB RAS
Siberian Federal University
Доп.точки доступа:
Novikov, A.E.; Новиков Антон Евгеньевич; Novikov, E.A.; Новиков Евгений Александрович; Levykin, A.I.; Левыкин Александр Иванович
Перевод заглавия: Численное моделирование химической кинетики двухстадийным методом решения неявных систем
Кл.слова (ненормированные):
Неявная система -- метод Розенброка -- контроль точности -- Implicit system -- Rosenbrock method -- accuracy control
Аннотация: The Cauchy problem for a stiff system of ODEs unresolved with respect to the derivative often arises in chemical kinetics, mechanical engineering, and other important applications. The two-stage L-stable Rosenbrock-type method is derived. An integration algorithm of alternating stepsize is designed based on the method, aimed at solving implicit stiff systems of ODEs. Numerical results confirming the efficiency of the new algorithm are given.
В химической кинетике, машиностроении и в других важных приложениях возникает задача Коши для жесткой системы ОДУ неразрешенных относительно производной. Построен двухстадийный L-устойчивый метод типа Розенброка, предназначенный для решения неявных жестких систем ОДУ. На основе этого метода сформулирован алгоритм интегрирования переменного шага. Приведены результаты расчетов, подтверждающие эффективность нового алгоритма.
РИНЦ
Держатели документа:
Institute of Computational Mathematics and Mathematical Geophysics SB RAS
Institute of computational modeling SB RAS
Siberian Federal University
Доп.точки доступа:
Novikov, A.E.; Новиков Антон Евгеньевич; Novikov, E.A.; Новиков Евгений Александрович; Levykin, A.I.; Левыкин Александр Иванович
Third Order (m, k)-Method for Solving Stiff Systems of ODEs and DAEs
/ A. I. Levykin, A. E. Novikov, E. A. Novikov // 2018 14th International Scientific-Technical Conference on Actual Problems of Electronic Instrument Engineering, APEIE 2018 - Proceedings : Institute of Electrical and Electronics Engineers Inc., 2018. - 14th International Scientific-Technical Conference on Actual Problems of Electronic Instrument Engineering, APEIE 2018 (2 October 2018 through 6 October 2018, ) Conference code: 143146. - P158-163, DOI 10.1109/APEIE.2018.8545974
. -
Кл.слова (ненормированные):
(m,k)-method -- DAE -- freezing the Jacobian matrix -- Electronics industry -- Freezing -- Ordinary differential equations -- (m,k)-method -- Cauchy problems -- Index systems -- L-stable -- Numerical results -- Step size -- Stiff systems -- Third order -- Jacobian matrices
Аннотация: The Cauchy problem for stiff systems of ODEs unresolved with respect to derivative arises in electrical engineering, chemical kinetics and other important areas. Authors derived an L-stable (5, 3)-method for solving the first index systems of DAEs. An algorithm of the alternating integration stepsize based on this method is formulated. The algorithm allows freezing the Jacobian matrix of the system to be solved. Numerical results confirming the efficiency of the new algorithm are given. © 2018 IEEE.
Scopus,
Смотреть статью
Держатели документа:
Institute of Computational Mathematics and Mathematical Geophysics, SB, RAS, Novosibirsk, Russian Federation
Siberian Federal University, Institute of Mathematics and Fundamental Informatics, Krasnoyarsk, Russian Federation
Institute of Computational Modelling, FRC KSC, SB, RAS, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Levykin, A. I.; Novikov, A. E.; Novikov, E. A.
Кл.слова (ненормированные):
(m,k)-method -- DAE -- freezing the Jacobian matrix -- Electronics industry -- Freezing -- Ordinary differential equations -- (m,k)-method -- Cauchy problems -- Index systems -- L-stable -- Numerical results -- Step size -- Stiff systems -- Third order -- Jacobian matrices
Аннотация: The Cauchy problem for stiff systems of ODEs unresolved with respect to derivative arises in electrical engineering, chemical kinetics and other important areas. Authors derived an L-stable (5, 3)-method for solving the first index systems of DAEs. An algorithm of the alternating integration stepsize based on this method is formulated. The algorithm allows freezing the Jacobian matrix of the system to be solved. Numerical results confirming the efficiency of the new algorithm are given. © 2018 IEEE.
Scopus,
Смотреть статью
Держатели документа:
Institute of Computational Mathematics and Mathematical Geophysics, SB, RAS, Novosibirsk, Russian Federation
Siberian Federal University, Institute of Mathematics and Fundamental Informatics, Krasnoyarsk, Russian Federation
Institute of Computational Modelling, FRC KSC, SB, RAS, Krasnoyarsk, Russian Federation
Доп.точки доступа:
Levykin, A. I.; Novikov, A. E.; Novikov, E. A.
Schemes of (m, k)-Type for Solving Differential-Algebraic and Stiff Systems
/ A. I. Levykin, A. E. Novikov, E. A. Novikov // Numer. Anal. Appl. - 2020. - Vol. 13, Is. 1. - P34-44, DOI 10.1134/S1995423920010036
. - ISSN 1995-4239
Кл.слова (ненормированные):
Jacobian matrices -- Computational costs -- Differential algebraic -- Integration algorithm -- Numerical results -- Numerical solution -- Stiff systems -- Type methods -- Variable step size -- Function evaluation
Аннотация: ABSTRACT: A form of Rosenbrock-type methods optimal in terms of the number ofnon-zero parameters and computational costs per step is considered. Atechnique of obtaining (m, k) -methodsfrom some well-known Rosenbrock-type methods is justified. Formulas fortransforming the parameters of (m, k) -schemesand for obtaining a stability function are given for two canonicalrepresentations of the schemes. An L-stable(3 , 2) -methodof order 3 is proposed, which requires two evaluations of the function:one evaluation of the Jacobian matrix and oneLU-decompositionper step. A variable step size integration algorithm based on the(3 , 2) -methodis formulated. It provides a numerical solution for both explicit andimplicit systems of ODEs. Numerical results are presented to show theefficiency of the new algorithm. © 2020, Pleiades Publishing, Ltd.
Scopus
Держатели документа:
Institute of Computational Mathematics and MathematicalGeophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation
Novosibirsk State University, Novosibirsk, 630090, Russian Federation
Siberian Federal University, Krasnoyarsk, 660041, Russian Federation
Institute of Computational Modeling, Siberian Branch,Russian Academy of Sciencess, Krasnoyarsk, 660036, Russian Federation
Доп.точки доступа:
Levykin, A. I.; Novikov, A. E.; Novikov, E. A.
Кл.слова (ненормированные):
Jacobian matrices -- Computational costs -- Differential algebraic -- Integration algorithm -- Numerical results -- Numerical solution -- Stiff systems -- Type methods -- Variable step size -- Function evaluation
Аннотация: ABSTRACT: A form of Rosenbrock-type methods optimal in terms of the number ofnon-zero parameters and computational costs per step is considered. Atechnique of obtaining (m, k) -methodsfrom some well-known Rosenbrock-type methods is justified. Formulas fortransforming the parameters of (m, k) -schemesand for obtaining a stability function are given for two canonicalrepresentations of the schemes. An L-stable(3 , 2) -methodof order 3 is proposed, which requires two evaluations of the function:one evaluation of the Jacobian matrix and oneLU-decompositionper step. A variable step size integration algorithm based on the(3 , 2) -methodis formulated. It provides a numerical solution for both explicit andimplicit systems of ODEs. Numerical results are presented to show theefficiency of the new algorithm. © 2020, Pleiades Publishing, Ltd.
Scopus
Держатели документа:
Institute of Computational Mathematics and MathematicalGeophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation
Novosibirsk State University, Novosibirsk, 630090, Russian Federation
Siberian Federal University, Krasnoyarsk, 660041, Russian Federation
Institute of Computational Modeling, Siberian Branch,Russian Academy of Sciencess, Krasnoyarsk, 660036, Russian Federation
Доп.точки доступа:
Levykin, A. I.; Novikov, A. E.; Novikov, E. A.