Valentin A. Gushchin, “On a one family of quasimonotone finite-difference schemes of the second order of approximation”, Mat. Model., 28:2 (2016), 6–18; Math. Models Comput. Simul., 8:5 (2016), 487

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Matematicheskoe modelirovanie, 2016, Volume 28, Number 2, Pages 6–18 (Mi mm3695)

This article is cited in 24 scientific papers (total in 24 papers)

On a one family of quasimonotone finite-difference schemes of the second order of approximation

Valentin A. Gushchin^ab

^a Institute for Computer Aided Design of the Russian Academy of Sciences
^b Moscow Institute of Physics and Technology

Full-text PDF (501 kB) Citations (24)

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Abstract: Using a simple model of a linear transport equation a family of hybrid monotone finite difference schemes has been constructed. By the analysis of the differential approximation it was shown that the resulting family has a second-order approximation in the spatial variable, has minimal scheme viscosity and dispersion and monotonous. It is shown that the region of operability of the base schemes (Modified Central Difference Schemes (MCDS) and Modified Upwind Difference Schemes (MUDS)) is a non-empty set. The local criterion for switching between the base schemes is based on the sign of the product of the velocity, the first and second differences of the transferred functions at the considered point. On the solution of the Cauchy problem provides a graphical comparison of the calculation results obtained using the known schemes of the first, second and third order approximation.

Keywords: finite difference schemes, monotonicity of finite difference schemes, hybrid finite difference schemes, criterion for switching.

Funding agency	Grant number
Russian Foundation for Basic Research	14-01-00428_а 15-51-50023_Яф_а
Russian Academy of Sciences - Federal Agency for Scientific Organizations

Received: 29.06.2015

English version:
Mathematical Models and Computer Simulations, 2016, Volume 8, Issue 5, Pages 487–496
DOI: https://doi.org/10.1134/S2070048216050094

Bibliographic databases:

Document Type: Article

UDC: 519.683

Language: Russian

Citation: Valentin A. Gushchin, “On a one family of quasimonotone finite-difference schemes of the second order of approximation”, Mat. Model., 28:2 (2016), 6–18; Math. Models Comput. Simul., 8:5 (2016), 487–496

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mm3695

https://www.mathnet.ru/eng/mm/v28/i2/p6

This publication is cited in the following 24 articles:

V A Gushchin, I A Smirnova, “Mathematical modeling of the vortices couple dynamics in a stratified fluid”, J. Phys.: Conf. Ser., 2910:1 (2024), 012029
V. A. Gushchin, I. A. Smirnova, THE 5TH INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE IN INFORMATION SYSTEMS (CIIS 2022): Intelligent and Resilient Digital Innovations for Sustainable Living, 2968, THE 5TH INTERNATIONAL CONFERENCE ON COMPUTATIONAL INTELLIGENCE IN INFORMATION SYSTEMS (CIIS 2022): Intelligent and Resilient Digital Innovations for Sustainable Living, 2023, 060003
V. A. Guschin, “Razrabotka i primenenie metoda rasschepleniya po fizicheskim faktoram dlya issledovaniya techenii neszhimaemoi zhidkosti”, Kompyuternye issledovaniya i modelirovanie, 14:4 (2022), 715–739
Alexander Sukhinov, Alexander Chistyakov, Elena Timofeeva, Alla Nikitina, Yulia Belova, “The Construction and Research of the Modified “Upwind Leapfrog” Difference Scheme with Improved Dispersion Properties for the Korteweg–de Vries Equation”, Mathematics, 10:16 (2022), 2922
Margarita N. Favorskaya, Ilia S. Nikitin, Natalia S. Severina, Smart Innovation, Systems and Technologies, 274, Advances in Theory and Practice of Computational Mechanics, 2022, 1
Elena Timofeeva, Aleksandr Sukhinov, Aleksandr Chistiakov, Nadezhda Timofeeva, Lecture Notes in Networks and Systems, 424, Mathematics and its Applications in New Computer Systems, 2022, 371
Alexander Sukhinov, Alexander Chistyakov, Inna Kuznetsova, Yulia Belova, Elena Rahimbaeva, “Development and Research of a Modified Upwind Leapfrog Scheme for Solving Transport Problems”, Mathematics, 10:19 (2022), 3564
Valentin A. Gushchin, Irina A. Smirnova, Smart Innovation, Systems and Technologies, 274, Advances in Theory and Practice of Computational Mechanics, 2022, 77
V. A. Gushchin, I. A. Smirnova, APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 13th International Hybrid Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS'21, 2522, APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 13th International Hybrid Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS'21, 2022, 080002
Valentin A. Gushchin, Vasilii G. Kondakov, Irina A. Smirnova, Smart Innovation, Systems and Technologies, 217, Applied Mathematics and Computational Mechanics for Smart Applications, 2021, 35
Valentin A. Gushchin, Smart Innovation, Systems and Technologies, 215, Smart Modelling for Engineering Systems, 2021, 25
A. I. Sukhinov, I. Yu. Kuznetsova, A. E. Chistyakov, E. A. Protsenko, Yu. V. Belova, “Studying the Accuracy and Applicability of the Finite Difference Scheme for Solving the Diffusion–Convection Problem at Large Grid Péclet Numbers”, J Appl Mech Tech Phy, 62:7 (2021), 1255
Gushchin V.A., Smirnova I.A., “On a Vortex Couple Dynamics in Fluid”, AIP Conference Proceedings, 2302, ed. Todorov M., Amer Inst Physics, 2020, 120006
A. I. Sukhinov, A. E. Chistyakov, E. A. Protsenko, A. M. Atayan, “Lineinaya kombinatsiya skhem «kabare» i «krest» s vesovymi koeffitsientami, poluchennymi iz usloviya minimizatsii poryadka pogreshnosti approksimatsii”, Chebyshevskii sb., 21:4 (2020), 243–256
V. A. Gushchin, I. A. Smirnova, “Mathematical modeling of spot dynamics in a stratified medium”, Comput. Math. Math. Phys., 60:5 (2020), 879–894
V A Gushchin, I A Smirnova, “On the formation of a vortex couple in fluid”, IOP Conf. Ser.: Mater. Sci. Eng., 927:1 (2020), 012050
Valentin A. Gushchin, Irina A. Smirnova, Smart Innovation, Systems and Technologies, 173, Advances in Theory and Practice of Computational Mechanics, 2020, 11
Lakhmi C. Jain, Margarita N. Favorskaya, Ilia S. Nikitin, Dmitry L. Reviznikov, Smart Innovation, Systems and Technologies, 173, Advances in Theory and Practice of Computational Mechanics, 2020, 1
A.I. Sukhinov, I.Y. Kuznetsova, A.E. Chistyakov, E.A. Protsenko, Y.V. Belova, “Study of the accuracy and applicability of the difference scheme for solving the diffusion-convection problem at large grid Péclet numbers”, Comp. Contin. Mech., 13:4 (2020), 437
A. I. Sukhinov, A. E. Chistyakov, “CABARET difference scheme with improved dispersion properties”, Math. Models Comput. Simul., 11:6 (2019), 867–876

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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