RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zh. Vychisl. Mat. Mat. Fiz., 2006, Volume 46, Number 9, Pages 1638–1667 (Mi zvmmf415)  

This article is cited in 48 scientific papers (total in 49 papers)

Monotonicity criteria for difference schemes designed for hyperbolic equations

A. S. Kholodovab, Ya. A. Kholodova

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

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.

Full text: PDF file (4589 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2006, 46:9, 1560–1588

Bibliographic databases:

UDC: 519.633
Received: 23.01.2006
Revised: 14.04.2006

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

Citation in format AMSBIB
\Bibitem{KhoKho06}
\by A.~S.~Kholodov, Ya.~A.~Kholodov
\paper Monotonicity criteria for difference schemes designed for hyperbolic equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2006
\vol 46
\issue 9
\pages 1638--1667
\mathnet{http://mi.mathnet.ru/zvmmf415}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2287663}
\elib{https://elibrary.ru/item.asp?id=9276148}
\transl
\jour Comput. Math. Math. Phys.
\yr 2006
\vol 46
\issue 9
\pages 1560--1588
\crossref{https://doi.org/10.1134/S0965542506090089}
\elib{https://elibrary.ru/item.asp?id=13514044}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33749009288}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf415
  • http://mi.mathnet.ru/eng/zvmmf/v46/i9/p1638

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. A. K. Bordonos, Ya. A. Kholodov, A. S. Kholodov, I. I. Morozov, “Modelirovanie globalnykh energeticheskikh setei”, Matem. modelirovanie, 21:6 (2009), 3–16  mathnet  zmath
    2. I. E. Kvasov, S. A. Pankratov, I. B. Petrov, “Computation of dynamic processes in continuous media with a crack initiated by the near-surface disturbance using grid-characteristic method”, Math. Models Comput. Simul., 3:3 (2011), 399–409  mathnet  crossref
    3. O. V. Geller, M. O. Vasilev, Ya. A. Kholodov, “Postroenie vysokoproizvoditelnogo vychislitelnogo kompleksa dlya modelirovaniya zadach gazovoi dinamiki”, Kompyuternye issledovaniya i modelirovanie, 2:3 (2010), 309–317  mathnet  crossref
    4. B. Yu. Krysanov, V. E. Kunitsyn, A. S. Kholodov, “MHD-based simulation of ionospheric perturbations generated in the atmospheric surface layer”, Comput. Math. Math. Phys., 51:2 (2011), 264–283  mathnet  crossref  mathscinet  isi  elib
    5. Rogov B.V., Mikhailovskaya M.N., “Monotone bicompact schemes for a linear advection equation”, Dokl. Math., 83:1 (2011), 121–125  crossref  mathscinet  zmath  isi  elib  elib  scopus
    6. B. V. Rogov, M. N. Mikhailovskaya, “The monotonic bicompact schemes for a linear transfer equation”, Math. Models Comput. Simul., 4:1 (2012), 92–100  mathnet  crossref  mathscinet  elib
    7. M. N. Mikhailovskaya, B. V. Rogov, “The bicompact monotonic schemes for a multidimensional linear transport equation”, Math. Models Comput. Simul., 4:3 (2012), 355–362  mathnet  crossref  mathscinet
    8. I. I. Morozov, A. V. Gasnikov, V. N. Tarasov, Ya. A. Kholodov, A. S. Kholodov, “Chislennoe issledovanie transportnykh potokov na osnove gidrodinamicheskikh modelei”, Kompyuternye issledovaniya i modelirovanie, 3:4 (2011), 389–412  mathnet  crossref
    9. I. E. Kvasov, I. B. Petrov, “High-performance computer simulation of wave processes in geological media in seismic exploration”, Comput. Math. Math. Phys., 52:2 (2012), 302–313  mathnet  crossref  zmath  adsnasa  isi  elib  elib
    10. Rogov B.V., “High-Order Accurate Running Compact Scheme for Multidimensional Hyperbolic Equations”, Dokl. Math., 86:1 (2012), 582–586  crossref  mathscinet  zmath  isi  elib  elib  scopus
    11. B. V. Rogov, “High-order accurate monotone compact running scheme for multidimensional hyperbolic equations”, Comput. Math. Math. Phys., 53:2 (2013), 205–214  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. A. I. Tolstykh, “Hybrid schemes with high-order multioperators for computing discontinuous solutions”, Comput. Math. Math. Phys., 53:9 (2013), 1303–1322  mathnet  crossref  crossref  isi  elib  elib
    13. V. I. Golubev, I. B. Petrov, N. I. Khokhlov, “Numerical simulation of seismic activity by the grid-characteristic method”, Comput. Math. Math. Phys., 53:10 (2013), 1523–1533  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    14. A. S. Kholodov, “Ob evolyutsii vozmuschenii, vyzvannykh dvizheniem meteoroidov v atmosfere Zemli”, Kompyuternye issledovaniya i modelirovanie, 5:6 (2013), 993–1030  mathnet  crossref
    15. I. B. Petrov, N. I. Khokhlov, “Modeling of 3D seismic problems using high-performance computing”, Math. Models Comput. Simul., 6:4 (2014), 342–350  mathnet  crossref
    16. I. B. Petrov, A. V. Favorskaya, N. I. Khokhlov, V. A. Miryaha, A. V. Sannikov, V. I. Golubev, “The monitoring state of a moving train using high performance systems and modern computational methods”, Math. Models Comput. Simul., 7:1 (2015), 51–61  mathnet  crossref
    17. Ya. A. Kholodov, A. E. Alekseenko, M. O. Vasilev, A. S. Kholodov, “Postroenie matematicheskoi modeli dorozhnogo perekrestka na osnove gidrodinamicheskogo podkhoda”, Kompyuternye issledovaniya i modelirovanie, 6:4 (2014), 503–522  mathnet  crossref
    18. V. I. Golubev, I. B. Petrov, N. I. Khokhlov, K. I. Shul'ts, “Numerical computation of wave propagation in fractured media by applying the grid-characteristic method on hexahedral meshes”, Comput. Math. Math. Phys., 55:3 (2015), 509–518  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    19. M. D. Bragin, B. V. Rogov, “Hybrid running schemes with upwind and bicompact symmetric differencing for hyperbolic equations”, Comput. Math. Math. Phys., 55:7 (2015), 1177–1187  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    20. E. N. Aristova, B. V. Rogov, A. V. Chikitkin, “Monotonization of high accuracy bicompact scheme for stationary multidimensional transport equation”, Math. Models Comput. Simul., 8:2 (2016), 108–117  mathnet  crossref  mathscinet  elib
    21. Khokhlov N.I. Petrov I.B., “on Bicompact Grid-Characteristic Schemes For the Linear Advection Equation”, Dokl. Math., 92:3 (2015), 781–783  crossref  mathscinet  zmath  isi  elib  scopus
    22. Khokhlov N. Yavich N. Malovichko M. Petrov I., “Solution of Large-Scale Seismic Modeling Problems”, 4Th International Young Scientist Conference on Computational Science, Procedia Computer Science, 66, ed. Sloot P. Boukhanovsky A. Athanassoulis G. Klimentov A., Elsevier Science BV, 2015, 191–199  crossref  isi  scopus
    23. Valentin A. Gushchin, “On a one family of quasimonotone finite-difference schemes of the second order of approximation”, Math. Models Comput. Simul., 8:5 (2016), 487–496  mathnet  crossref  elib
    24. V. I. Golubev, I. B. Petrov, N. I. Khokhlov, “Compact grid-characteristic schemes of higher orders for 3D linear transport equation”, Math. Models Comput. Simul., 8:5 (2016), 577–584  mathnet  crossref  elib
    25. A. V. Favorskaya, I. B. Petrov, “The study of increased order grid-characteristic methods on unstructured grids”, Num. Anal. Appl., 9:2 (2016), 171–178  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    26. E. N. Aristova, B. V. Rogov, A. V. Chikitkin, “Optimal monotonization of a high-order accurate bicompact scheme for the nonstationary multidimensional transport equation”, Comput. Math. Math. Phys., 56:6 (2016), 962–976  mathnet  crossref  crossref  isi  elib
    27. M. D. Bragin, B. V. Rogov, “Minimal dissipation hybrid bicompact schemes for hyperbolic equations”, Comput. Math. Math. Phys., 56:6 (2016), 947–961  mathnet  crossref  crossref  isi  elib
    28. V. A. Biryukov, V. A. Miryaha, I. B. Petrov, N. I. Khokhlov, “Simulation of elastic wave propagation in geological media: Intercomparison of three numerical methods”, Comput. Math. Math. Phys., 56:6 (2016), 1086–1095  mathnet  crossref  crossref  isi  elib
    29. A. E. Alekseenko, A. S. Kholodov, Ya. A. Kholodov, “Boundary control problems for quasilinear systems of hyperbolic equations”, Comput. Math. Math. Phys., 56:6 (2016), 916–931  mathnet  crossref  crossref  isi  elib
    30. Ya. A. Kholodov, M. O. Vasiliev, A. S. Kholodov, I. V. Tsybulin, “Developing the mathematical model for fine impurities spreading in ventilation networks”, Math. Models Comput. Simul., 9:2 (2017), 142–154  mathnet  crossref  elib
    31. I. E. Kvasov, V. B. Leviant, I. B. Petrov, “Numerical study of wave propagation in porous media with the use of the grid-characteristic method”, Comput. Math. Math. Phys., 56:9 (2016), 1620–1630  mathnet  crossref  crossref  isi  elib
    32. Khokhlov N.I., Petrov I.B., “On one class of high-order compact grid-characteristic schemes for linear advection”, Russ. J. Numer. Anal. Math. Model, 31:6 (2016), 355–368  crossref  mathscinet  zmath  isi  scopus
    33. Favorskaya A. Petrov I. Khokhlov N., “Numerical Modeling of Wave Processes During Shelf Seismic Exploration”, Knowledge-Based and Intelligent Information & Engineering Systems: Proceedings of the 20Th International Conference Kes-2016, Procedia Computer Science, 96, ed. Howlett R. Jain L. Gabrys B. Toro C. Lim C., Elsevier Science BV, 2016, 920–929  crossref  isi  scopus
    34. Petrov I., “Computational problems in Arctic Research”, International Conference on Computer Simulation in Physics and Beyond 2015, Journal of Physics Conference Series, 681, IOP Publishing Ltd, 2016, 012026  crossref  isi  scopus
    35. D. P. Grigorevykh, N. I. Khokhlov, I. B. Petrov, “Raschet dinamicheskogo razrusheniya v tverdykh deformiruemykh telakh”, Matem. modelirovanie, 29:4 (2017), 45–58  mathnet  elib
    36. A. V. Favorskaya, V. I. Golubev, “O primenenii formuly Releya na osnove integralnykh vyrazhenii Kirkhgofa k zadacham georazvedki”, Kompyuternye issledovaniya i modelirovanie, 9:5 (2017), 761–771  mathnet  crossref
    37. Stognii P.V. Petrov D.I. Khokhlov N.I. Petrov I.B., “Simulation of Seismic Processes in Geological Exploration of Arctic Shelf”, Russ. J. Numer. Anal. Math. Model, 32:6 (2017), 381–392  crossref  mathscinet  zmath  isi  scopus
    38. I. B. Petrov, “Problemy modelirovaniya prirodnykh i antropogennykh protsessov v Arkticheskoi zone Rossiiskoi Federatsii”, Matem. modelirovanie, 30:7 (2018), 103–136  mathnet
    39. P. V. Stognii, D. I. Petrov, N. I. Khokhlov, I. B. Petrov, “Chislennoe modelirovanie setochno-kharakteristicheskim metodom vliyaniya ledovykh obrazovanii na seismicheskie otkliki”, Matem. modelirovanie, 30:8 (2018), 107–115  mathnet
    40. Favorskaya A.V. Petrov I.B., “Theory and Practice of Wave Processes Modelling”, Innovations in Wave Processes Modelling and Decision Making: Grid-Characteristic Method and Applications, Smart Innovation Systems and Technologies, 90, ed. Favorskaya A. Petrov I., Springer-Verlag Berlin, 2018, 1–6  crossref  mathscinet  isi  scopus
    41. A. I. Lobanov, “Nauchnye i pedagogicheskie shkoly Aleksandra Sergeevicha Kholodova”, Kompyuternye issledovaniya i modelirovanie, 10:5 (2018), 561–579  mathnet  crossref
    42. A. M. Ivanov, N. I. Khokhlov, “Parallelnaya realizatsiya setochno-kharakteristicheskogo metoda v sluchae yavnogo vydeleniya kontaktnykh granits”, Kompyuternye issledovaniya i modelirovanie, 10:5 (2018), 667–678  mathnet  crossref
    43. Ya. A. Kholodov, A. S. Kholodov, I. V. Tsybulin, “Construction of monotone difference schemes for systems of hyperbolic equations”, Comput. Math. Math. Phys., 58:8 (2018), 1226–1246  mathnet  crossref  crossref  isi  elib
    44. A. V. Vasyukov, I. B. Petrov, “Grid-characteristic method on tetrahedral unstructured meshes with large topological inhomogeneities”, Comput. Math. Math. Phys., 58:8 (2018), 1259–1269  mathnet  crossref  crossref  isi  elib
    45. M. E. Ladonkina, O. A. Neklyudova, V. V. Ostapenko, V. F. Tishkin, “On the accuracy of the discontinuous Galerkin method in calculation of shock waves”, Comput. Math. Math. Phys., 58:8 (2018), 1344–1353  mathnet  crossref  crossref  isi  elib
    46. V. I. Golubev, O. Ya. Voinov, I. B. Petrov, “Seismic imaging of fractured elastic media on the basis of the grid-characteristic method”, Comput. Math. Math. Phys., 58:8 (2018), 1309–1315  mathnet  crossref  crossref  isi  elib
    47. Ya. A. Kholodov, “Razrabotka setevykh vychislitelnykh modelei dlya issledovaniya nelineinykh volnovykh protsessov na grafakh”, Kompyuternye issledovaniya i modelirovanie, 11:5 (2019), 777–814  mathnet  crossref
    48. A. V. Favorskaya, I. B. Petrov, “Raschet setochno-kharakteristicheskim metodom razrusheniya mnogoetazhnykh zdanii”, Matem. modelirovanie, 32:3 (2020), 102–114  mathnet  crossref
    49. A. I. Lobanov, F. Kh. Mirov, “Raznostnye skhemy dlya uravneniya perenosa so stokom na osnove analiza v prostranstve neopredelennykh koeffitsientov”, Matem. modelirovanie, 32:9 (2020), 53–72  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:844
    Full text:388
    References:59
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020