Abstract:
We consider some principles for construction of the time integration schemes for parabolic equations. It is presented an approach based on explicit iterations with Chebyshev parameters and resulting in the schemes of the first and second order of accuracy. This paper gives systematization of knowledge of these schemes, conditions of their applicability, included applications for computations of high temperature processes in thermonuclear targets.
Citation:
V. T. Zhukov, “On explicit methods for the time integration of parabolic equations”, Mat. Model., 22:10 (2010), 127–158; Math. Models Comput. Simul., 3:3 (2011), 311–332
\Bibitem{Zhu10}
\by V.~T.~Zhukov
\paper On explicit methods for the time integration of parabolic equations
\jour Mat. Model.
\yr 2010
\vol 22
\issue 10
\pages 127--158
\mathnet{http://mi.mathnet.ru/mm3034}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2809075}
\transl
\jour Math. Models Comput. Simul.
\yr 2011
\vol 3
\issue 3
\pages 311--332
\crossref{https://doi.org/10.1134/S2070048211030136}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925938288}
Linking options:
https://www.mathnet.ru/eng/mm3034
https://www.mathnet.ru/eng/mm/v22/i10/p127
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E. E. Peskova, O. S. Yazovtseva, E. Yu. Makarova, N. A. Tingaeva, Communications in Computer and Information Science, 1914, Mathematical Modeling and Supercomputer Technologies, 2024, 112
E. E. Peskova, O. S. Yazovtseva, “Application of the Explicitly Iterative Scheme to Simulating Subsonic Reacting Gas Flows”, Comput. Math. and Math. Phys., 64:2 (2024), 326
M. A. Botchev, V. T. Zhukov, “Adaptive Iterative Explicit Time Integration for Nonlinear Heat Conduction Problems”, Lobachevskii J Math, 45:1 (2024), 12
M. A. Botchev, “On convergence of waveform relaxation for nonlinear systems of ordinary differential equations”, Calcolo, 61:2 (2024)
M. A. Botchev, I. A. Fahurdinov, E. B. Savenkov, “Efficient and Stable Time Integration of Cahn–Hilliard Equations: Explicit, Implicit, and Explicit Iterative Schemes”, Comput. Math. and Math. Phys., 64:8 (2024), 1726
V. T. Zhukov, O. B. Feodoritova, “Scheme for Calculating Unsteady Flows of Heat-Conducting Gas in the Three-Temperature Approximation”, Comput. Math. and Math. Phys., 64:8 (2024), 1840
M. A. Botchev, I. A. Fakhrutdinov, E. B. Savenkov, “Efficient and stable time integration of Cahn–Hilliard equations: explicit, implicit, and explicit iterative schemes”, Comput. Math. Math. Phys., 64:8 (2024), 1726–1746
V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “O pryamom metode resheniya zadachi sopryazhennogo teploobmena gazovoi smesi i tverdogo tela”, Preprinty IPM im. M. V. Keldysha, 2023, 012, 36 pp.
A. A. Bai, “Modelirovanie vzaimodeistviya lazernogo izlucheniya s kriogennoi vodorodnoi plenkoi na octree-setkakh blochnogo tipa”, Preprinty IPM im. M. V. Keldysha, 2023, 060, 24 pp.
M. A. Bochev, V. T. Zhukov, “Eksponentsialnaya i neyavnaya skhemy Eilera dlya resheniya nelineinykh zadach teploprovodnosti”, Preprinty IPM im. M. V. Keldysha, 2023, 069, 16 pp.
M. A. Botchev, V. T. Zhukov, “Exponential Euler and Backward Euler Methods for Nonlinear Heat Conduction Problems”, Lobachevskii J Math, 44:1 (2023), 10
P.P. Zakharov, N.N. Smirnov, A.B. Kiselev, “Numerical modelling of high velocity impact problem involving non-linear viscosity”, Acta Astronautica, 212 (2023), 398
O. B. Feodoritova, N. D. Novikova, V. T. Zhukov, “Development of Numerical Methodology for Unsteady Fluid–Solid Thermal Interaction in Multicomponent Flow Simulation”, Lobachevskii J Math, 44:1 (2023), 33
V. T. Zhukov, N. D. Novikova, O. B. Feodoritova, “On one method for calculating nonstationary heat transfer between a gas flow and a solid body”, Comput. Math. Math. Phys., 63:12 (2023), 2344–2358
V. E. Borisov, B. V. Kritskii, Yu. G. Rykov, “Programmnyi modul MCFL-Chem dlya rascheta vysokoskorostnykh techenii smesi reagiruyuschikh gazov”, Preprinty IPM im. M. V. Keldysha, 2022, 021, 40 pp.
B. N. Chetverushkin, O. G. Olkhovskaya, V. A. Gasilov, “An explicit difference scheme for non-linear heat conduction equation”, Math. Models Comput. Simul., 15:3 (2023), 529–538
M. A. Botchev, “Solving anisotropic heat equations by exponential shift-and-invert and polynomial Krylov subspace methods”, Keldysh Institute preprints, 2022, 4–17
M.A. Botchev, “Solving anisotropic heat equations by exponential shift-and-invert and polynomial Krylov subspace methods”, J. Phys.: Conf. Ser., 2028:1 (2021), 012021
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