A. S. Kholodov, Ya. A. Kholodov, “Monotonicity criteria for difference schemes designed for hyperbolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 46:9 (2006), 1638–1667; Comput. Math. Math. Phys., 46:9 (2006), 1560

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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 9, Pages 1638–1667 (Mi zvmmf415)

This article is cited in 88 scientific papers (total in 89 papers)

Monotonicity criteria for difference schemes designed for hyperbolic equations

A. S. Kholodov^ab, Ya. A. Kholodov^a

^a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia
^b Institute for Computer-Aided Design, Russian Academy of Sciences, Vtoraya Brestskaya ul. 19/18, Moscow, 123056, Russia

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Abstract: Previously formulated monotonicity criteria for explicit two-level difference schemes designed for hyperbolic equations (S. K. Godunov's, A. Harten's (TVD schemes), characteristic criteria) are extended to multileveled, including implicit, stencils. The characteristic monotonicity criterion is used to develop a universal algorithm for constructing high-order accurate nonlinear monotone schemes (for an arbitrary form of the desired solution) based on their analysis in the space of grid functions. Several new fourth-to-third-order accurate monotone difference schemes on a compact three-level stencil and nonexpanding (three-point) stencils are proposed for an extended system, which ensures their monotonicity for both the desired function and its derivatives. The difference schemes are tested using the characteristic monotonicity criterion and are extended to systems of hyperbolic equations.

Key words: hyperbolic equations, difference schemes, monotonicity criteria for difference schemes, high-order accurate difference schemes.

Received: 23.01.2006
Revised: 14.04.2006

English version:
Computational Mathematics and Mathematical Physics, 2006, Volume 46, Issue 9, Pages 1560–1588
DOI: https://doi.org/10.1134/S0965542506090089

Bibliographic databases:

Document Type: Article

UDC: 519.633

Language: Russian

Citation: A. S. Kholodov, Ya. A. Kholodov, “Monotonicity criteria for difference schemes designed for hyperbolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 46:9 (2006), 1638–1667; Comput. Math. Math. Phys., 46:9 (2006), 1560–1588

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Linking options:

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This publication is cited in the following 89 articles:

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Evgeniya K. Guseva, Vasily I. Golubev, Viktor P. Epifanov, Igor B. Petrov, Communications in Computer and Information Science, 1914, Mathematical Modeling and Supercomputer Technologies, 2024, 15
M. D. Bragin, “Actual Accuracy of Linear Schemes of High-Order Approximation in Gasdynamic Simulations”, Comput. Math. and Math. Phys., 64:1 (2024), 138
A. Yu. Trynin, “On One Method for Solving a Mixed Boundary Value Problem for a Parabolic Type Equation Using Operators $\mathbb{A}{{\mathbb{T}}_{{\lambda ,j}}}$”, Russ Math., 68:2 (2024), 52
E. K. Guseva, V. I. Golubev, I. B. Petrov, “Investigation of Wave Phenomena During the Seismic Survey in the Permafrost Areas Using Two Approaches to Numerical Modeling”, Lobachevskii J Math, 45:1 (2024), 231
E. K. Guseva, V. I. Golubev, I. B. Petrov, “Investigation of Wave Phenomena in the Offshore Areas of the Arctic Region in the Process of the Seismic Survey”, Lobachevskii J Math, 45:1 (2024), 223
Epifanov Viktor Pavlovich, Guseva Evgeniya Kirillovna, Shigaev Nikita Olegovich, Springer Proceedings in Earth and Environmental Sciences, Proceedings of the 9th International Conference on Physical and Mathematical Modelling of Earth and Environmental Processes, 2024, 275
I. B. Petrov, E. K. Guseva, V. I. Golubev, V. P. Epifanov, “Ice rheology exploration based on numerical simulation of low-speed impact”, Doklady Rossijskoj akademii nauk. Fizika, tehničeskie nauki, 514:1 (2024), 20
A. V. Favorskaya, I. B. Petrov, “Simulation of Seismic Impact on Multistory Buildings on Piles by Grid-Characteristic Method on Cartesian and Nonconformal Curved Meshes”, Math Models Comput Simul, 16:S1 (2024), S56
V. E. Karpov, A. I. Lobanov, “Setochno-kharakteristicheskaya raznostnaya skhema dlya resheniya uravneniya Khopfa na osnove dvukh razlichnykh divergentnykh form”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 16:2 (2023), 91–103
E. K. Guseva, V. I. Golubev, I. B. Petrov, “Lineinye kvazimonotonnye i gibridnye setochno-kharakteristicheskie skhemy dlya chislennogo resheniya zadach lineinoi akustiki”, Sib. zhurn. vychisl. matem., 26:2 (2023), 135–147
A. Yu. Trynin, “A method for solution of a mixed boundary value problem for a hyperbolic type equation using the operators $\mathbb{AT}_{\lambda,j}$”, Izv. Math., 87:6 (2023), 1227–1254
A. Yu. Trynin, “On a method for solving a mixed boundary value problem for a parabolic equation using modified sinc-approximation operators”, Comput. Math. Math. Phys., 63:7 (2023), 1264–1284
I. B. Petrov, V. I. Golubev, A. V. Shevchenko, I. S. Nikitin, “About the boundary condition approximation in the higher-order grid-characteristic schemes”, Dokl. Math., 108:3 (2023), 466–471
E. K. Guseva, V. I. Golubev, I. B. Petrov, “Linear Quasi-Monotone and Hybrid Grid-Characteristic Schemes for the Numerical Solution of Linear Acoustic Problems1”, Numer. Analys. Appl., 16:2 (2023), 112
I. B. Petrov, “Grid-characteristic methods. 55 years of developing and solving complex dynamic problems”, CMIT, 6:1 (2023), 6
E. K. Guseva, V. I. Golubev, I. B. Petrov, “Linear, Quasi-Monotonic and Hybrid Grid-Characteristic Schemes for Hyperbolic Equations”, Lobachevskii J Math, 44:1 (2023), 296
V. I Golubev, I. S Nikitin, N. G Burago, Yu. A Golubeva, “Yavno-neyavnye skhemy rascheta dinamiki uprugovyazkoplasticheskikh sred s malym vremenem relaksatsii”, Differentsialnye uravneniya, 59:6 (2023), 803
N. I. Khokhlov, I. B. Petrov, “High-Order Grid-Characteristic Method for Systems of Hyperbolic Equations with Piecewise Constant Coefficients”, Diff Equat, 59:7 (2023), 985
V. I. Golubev, I. S. Nikitin, N. G. Burago, Yu. A. Golubeva, “Explicit–Implicit Schemes for Calculating the Dynamics of Elastoviscoplastic Media with a Short Relaxation Time”, Diff Equat, 59:6 (2023), 822

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