Учредитель Федеральное государственное автономное образовательное
учреждение высшего образования
Южно-Уральский государственный университет
(национальный исследовательский университет)≫
≪
Основной целью издания является пропаганда союза качественных и численных исследований
математических моделей. Предпочтение при публикации будут иметь статьи, посвященные
результатам качественных исследований математических моделей, выявляющих
какие-либо неочевидные их свойства; результатам численных исследований, содержащих
разработки новых вычислительных алгоритмов применительно к математическим моделям;
и комплексам программ, созданным для постановки вычислительных экспериментов.
Редакционная коллегия
ê.ô.-ì.í., ïðîô. Заляпин Â.È.,
ä.ô.-ì.í., äîö. Замышляева À.À.,
ä.ô.-ì.í., äîö. Келлер À.Â.,
ä.ô.-ì.í., äîö. Манакова Í.À.
(отв. секретарь),
ä.ô.-ì.í., ïðîô. Свиридюк Ã.À.
(гл. редактор)
Редакционный совет
ïðîô., ä-ð Аббас Ñ.,
ä.ô.-ì.í., ïðîô. Банасяк ß.,
ä.ò.í., ïðîô. Богомолов À.Â.,
ä.ô.-ì.í. Бржезинская Ì.Ì.,
ä.ò.í., ïðîô. Володарский Å.Ò.,
ïðîô., ä-ð Вонг Ï.,
ïðîô., ä-ð Йонг Ëè,
ä.ô.-ì.í., ïðîô. Кадченко Ñ.È.,
ä.ô.-ì.í., àêàä. НАН Республики
Казахстан Кальменов Т.Ш.,
ä.ô.-ì.í., äîö. Корпусов Ì.Î.,
ä.ò.í., ÷ë.-êîð. РАН Новиков Ä.À.
(председатель),
ä.ò.í., ñ.í.ñ. Поляк Á.Ò.,
ä.ô.-ì.í., ïðîô. Пятков Ñ.Ã.,
ä.ò.í., ïðîô. Радев Õ.Ê.,
ïðîô., ä-ð Ривера Æ.Å.Ì.,
ä.ô.-ì.í., ïðîô. Сапронов Þ.È.,
ïðîô., ä-ð Tà Зуй Ôûîíã,
ïðîô., ä-ð Тиба Ä.,
ä.ò.í., ïðîô. Уткин Ë.Â.,
ïðîô., ä-ð Фавини À.,
ä.ô.-ì.í., ïðîô. Фурсиков À.Â.,
ä.ô.-ì.í., ÷ë.-êîð. РАН Ченцов À.Ã.
⃝c Издательский центр ÞÓðÃÓ, 2018
Стр.3
South Ural State University
Main purpose of the publication is to promote the union of the qualitative of numerical studies of
mathematical models. Articles, devoted to the results of qualitative studies of mathematical models, that
identify any non-obvious properties, the results of numerical studies that contain the development of
new computational algorithms applied for the computational experiments, will have the preference for
publication.
Editorial Board
A.V. Keller, South Ural State University, Chelyabinsk, Russian Federation
N.A. Manakova, South Ural State University, Chelyabinsk, Russian Federation
G.A. Sviridyuk, South Ural State University, Chelyabinsk, Russian Federation
V.I. Zalyapin, South Ural State University, Chelyabinsk, Russian Federation
A.A. Zamyshlyaeva, South Ural State University, Chelyabinsk, Russian Federation
Editorial Council
S. Abbas, Indian Institute of Technology Mandi, Mandi, India
J. Banasiak, University of Pretoria, Pretoria, Republic of South Africa
A.V. Bogomolov, Military Academy of the General Sta of the RF Armed Forces, Moscow,
Russian Federation
M.M. Brzhezinskaya, Helmholtz-Zentrum Berlin for Materials and Energy, Berlin, Germany
A.G. Chentsov, Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the RAS,
Yekaterinburg, Russian Federation
A.V. Fursikov, Lomonosov Moscow State University, Moscow, Russian Federation
A. Favini, University of Bologna, Bologna, Italy
S.I. Kadchenko, Nosov Magnitogorsk State Technical University, Magnitogorsk, Russian Federation
T.Sh. Kal'menov, Institute of Mathematics and Mathematical Modelling, Almaty, Kazakhstan
M.O. Korpusov, Lomonosov Moscow State University, Moscow, Russian Federation
D.A. Novikov, V.A. Trapeznikov Institute of Control Sciences of the RAS, Moscow, Russian Federation
B.T. Polyak, V.A. Trapeznikov Institute of Control Sciences of the RAS, Moscow, Russian Federation
S.G. Pyatkov, Sobolev Institute of Mathematics, Siberian Branch of the RAS, Novosibirsk,
Russian Federation
H.K. Radev, Technical University of So a, So a, Bulgaria
J.E.M. Rivera, Federal University of Rio de Janeiro, Institute of Mathematic, Rio de Janeiro, Brazil
Yu.I. Sapronov, Voronezh State University, Voronezh, Russian Federation
Ta Duy Phuong, Hanoi Institute of Mathematics, Hanoi, Vietnam
D. Tiba, Institute of Mathematics Romanian Academy, Bucharest, Romania
E.T. Volodarskiy, National Technical University, Kiev, Ukraine
L.V. Utkin, Peter the Great Saint-Petersburg Polytechnic University, Saint Petersburg,
Russian Federation
P.J.Y. Wong, Nanyang Technological University, School of Electrical and Electronic Engineering,
Singapore, Singapore
Yong Li, College of Electrical and Information Engineering, Hunan University, Changsha, China
76, Lenin ave, Chelyabinsk, 454080, Russian Federation, vestnik@susu.ru, mmp.vestnik.susu.ru
Стр.4
Содержание
Математическое моделирование
THE CAUCHY PROBLEM FOR THE SOBOLEV TYPE EQUATION OF HIGHER ORDER
A.A. Zamyshlyaeva, E.V. Bychkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
RELAY RACES ALONG A PAIR OF SELECTABLE ROUTES
E.V. Larkin, A.V. Bogomolov, A.N. Privalov, N.N. Dobrovolsky . . . . . . . . . . . . . . . . . . . 15
OPTIMIZATION OF TRAINING MODULES CHOICE DURING MULTIPURPOSE
TRAINING OF SPECIALISTS
V.V. Menshikh, E.N. Sereda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
STABLE IDENTIFICATION OF LINEAR AUTOREGRESSIVE MODEL
WITH EXOGENOUS VARIABLES ON THE BASIS OF THE GENERALIZED
LEAST ABSOLUTE DEVIATION METHOD
A.V. Panyukov, Ya.A. Mezaal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
INVERSE PROBLEMS FOR MATHEMATICAL MODELS
OF QUASISTATIONARY ELECTROMAGNETIC WAVES IN ANISOTROPIC
NONMETALLIC MEDIA WITH DISPERSION
S.G. Pyatkov, S.N. Shergin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
SOLVING A ROUTING PROBLEM WITH THE AID OF AN INDEPENDENT
COMPUTATIONS SCHEME
A.G. Chentsov, A.M. Grigoryev, A.A. Chentsov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Программирование
ALGORITHM OF EFFECTIVE TRANSPORTATION WORK FOR CARGO TRAFFIC
M.V. Buyanov, A.I. Kibzun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
ПРОГРАММНЫЙ КОМПЛЕКС TEDY ДЛЯ РЕШЕНИЯ ЗАДАЧ
ТЕРМОДИНАМИЧЕСКОГО МОДЕЛИРОВАНИЯ
È.Â. Ïåøêè÷åâ, È.Ð. Ìàêååâà, Î.Â. Øóëüö, Â.Þ. Ïóãà÷åâ, Â.Ã. Дубосарский,
À.Å. Ïàóêîâà, Î.Â. Кузнецова, Ë.Í. Äàðèíà, À.À. Бочкарева . . . . . . . . . . . . . . . . . . . 84
NEW APPROXIMATE METHOD FOR SOLVING THE STOKES PROBLEM IN A DOMAIN
WITH CORNER SINGULARITY
V.A. Rukavishnikov, A.V. Rukavishnikov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
АНАЛИЗ ЭФФЕКТИВНОСТИ ФОТОГРАММЕТРИЧЕСКОЙ СИСТЕМЫ МЕТОДАМИ
ИМИТАЦИОННОГО МОДЕЛИРОВАНИЯ
Ñ.À. Òóøåâ, Á.Ì. Суховилов . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
NEW FEATURES OF PARALLEL IMPLEMENTATION OF N-BODY PROBLEMS ON GPU
S.S. Khrapov, S.A. Khoperskov, A.V. Khoperskov . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Краткие сообщения
ОСОБЕННОСТИ ЗАДАНИЯ ГРАНИЧНЫХ УСЛОВИЙ ПРИ МОДЕЛИРОВАНИИ
СЕТЧАТЫХ АНИЗОГРИДНЫХ КОНСТРУКЦИЙ
Ò.Â. Бурнышева, Î.À. Штейнбрехер, À.Ä. Ульянов . . . . . . . . . . . . . . . . . . . . . . . . . 137
ЧИСЛЕННЫЙ МЕТОД РЕШЕНИЯ КОЭФФИЦИЕНТНОЙ ОБРАТНОЙ ЗАДАЧИ
ДЛЯ НЕЛИНЕЙНОГО УРАВНЕНИЯ ДИФФУЗИИ РЕАКЦИИ
Õ.Ì. Гамзаев . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
APPROXIMATION OF THE SOLUTION SET FOR A SYSTEM OF NONLINEAR
INEQUALITIES FOR MODELING A ONE-DIMENSIONAL CHAOTIC PROCESS
A.S. Sheludko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Вестник ЮУрГУ. Серия ≪
и программирование≫
Математическое моделирование
(Âåñòíèê ЮУрГУ ÌÌÏ). 2018. Ò. 11, 1
Стр.5
Contents
Mathematical Modelling
THE CAUCHY PROBLEM FOR THE SOBOLEV TYPE EQUATION OF HIGHER ORDER
A.A. Zamyshlyaeva, E.V. Bychkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
RELAY RACES ALONG A PAIR OF SELECTABLE ROUTES
E.V. Larkin, A.V. Bogomolov, A.N. Privalov, N.N. Dobrovolsky . . . . . . . . . . . . . . . . . . . 15
OPTIMIZATION OF TRAINING MODULES CHOICE DURING MULTIPURPOSE
TRAINING OF SPECIALISTS
V.V. Menshikh, E.N. Sereda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
STABLE IDENTIFICATION OF LINEAR AUTOREGRESSIVE MODEL
WITH EXOGENOUS VARIABLES ON THE BASIS OF THE GENERALIZED
LEAST ABSOLUTE DEVIATION METHOD
A.V. Panyukov, Ya.A. Mezaal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
INVERSE PROBLEMS FOR MATHEMATICAL MODELS
OF QUASISTATIONARY ELECTROMAGNETIC WAVES IN ANISOTROPIC
NONMETALLIC MEDIA WITH DISPERSION
S.G. Pyatkov, S.N. Shergin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
SOLVING A ROUTING PROBLEM WITH THE AID OF AN INDEPENDENT
COMPUTATIONS SCHEME
A.G. Chentsov, A.M. Grigoryev, A.A. Chentsov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Programming & Computer Software
ALGORITHM OF EFFECTIVE TRANSPORTATION WORK FOR CARGO TRAFFIC
M.V. Buyanov, A.I. Kibzun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
SOFTWARE TEDY FOR THERMODYNAMICAL MODELLING
I.V. Peshkichev, I.R. Makeyeva, O.V. Shults, V.Yu. Pugachev, V.G. Dubosarskiy,
A.E. Paukova, O.V. Kuznetsova, L.N. Darina, A.A. Bochkareva . . . . . . . . . . . . . . . . . . . 84
NEW APPROXIMATE METHOD FOR SOLVING THE STOKES PROBLEM IN A DOMAIN
WITH CORNER SINGULARITY
V.A. Rukavishnikov, A.V. Rukavishnikov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
EFFICIENCY ANALYSIS OF PHOTOGRAMMETRIC SYSTEM
BY SIMULATION MODELLING
S.A. Tushev, B.M. Sukhovilov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
NEW FEATURES OF PARALLEL IMPLEMENTATION OF N-BODY PROBLEMS ON GPU
S.S. Khrapov, S.A. Khoperskov, A.V. Khoperskov . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Short Notes
FEATURES OF THE BOUNDARY CONDITIONS IN THE MODELLING MESH
DESIGNS ANIZOGRIDNYH
T.V. Burnysheva, O.A. Shteinbreher, A.D. Ulyanov . . . . . . . . . . . . . . . . . . . . . . . . . . 137
A NUMERICAL METHOD OF SOLVING THE COEFFICIENT
INVERSE PROBLEM FOR THE NONLINEAR EQUATION
OF DIFFUSION-REACTION
Kh. M. Gamzaev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
APPROXIMATION OF THE SOLUTION SET FOR A SYSTEM OF NONLINEAR
INEQUALITIES FOR MODELING A ONE-DIMENSIONAL CHAOTIC PROCESS
A.S. Sheludko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
Bulletin of the South Ural State University. Ser. Mathematical Modelling, Programming
& Computer Software (Bulletin SUSU MMCS), 2018, vol. 11, no. 1
Стр.6