Zobrazeno 1 - 10
of 71
pro vyhledávání: '"A. M. Evstigneev"'
Autor:
Nikolay M. Evstigneev, Oleg I. Ryabkov
Publikováno v:
Mathematics, Vol 11, Iss 20, p 4336 (2023)
In many physical systems, it is important to know the exact trajectory of a solution. Relevant applications include celestial mechanics, fluid mechanics, robotics, etc. For cases where analytical methods cannot be applied, one can use computer-assist
Externí odkaz:
https://doaj.org/article/6560949c7e194d42a093075d8a70e6c6
Publikováno v:
Mathematics, Vol 11, Iss 18, p 3875 (2023)
The analysis of bifurcations and chaotic dynamics for nonlinear systems of a large size is a difficult problem. Analytical and numerical approaches must be used to deal with this problem. Numerical methods include solving some of the hardest problems
Externí odkaz:
https://doaj.org/article/9905da823b5744988f8acc83d579d1aa
Publikováno v:
Differential Equations. 57:391-407
Using interval Taylor models (TM), we construct algorithms for the computer-assisted proof of the existence of periodic trajectories in systems of ordinary differential equations (ODEs). Although TMs allow one to construct guaranteed estimates for fa
Autor:
N. M. Evstigneev, N. A. Magnitskii
Publikováno v:
Doklady Mathematics. 101:110-114
This paper summarizes the results of studies of the laminar–turbulent transition in some fluid and gas dynamics problems obtained by applying numerical methods and methods of chaotic dynamics. The following problems are analyzed: 2D and 3D Kolmogor
Publikováno v:
Advances in Water Resources. 171:104340
Publikováno v:
Journal of Applied Nonlinear Dynamics. 8:595-619
A three dimensional Kolmogorov problem with extended forcing term for Navier-Stokes equations is considered in the extended periodic domain. The Galerkin{Fourier method is applied and two problem congurations are considered: the symmetry preserving s
Autor:
N. M. Evstigneev, O. I. Ryabkov
Publikováno v:
Differential Equations. 55:1198-1217
This work continues the research devoted to considering interval Taylor models (TM) as applied to proving the existence of periodic trajectories in systems of ordinary differential equations (ODEs). The Taylor models are used here within a topologica
Autor:
O. I. Ryabkov, N. M. Evstigneev
Publikováno v:
Communications in Computer and Information Science ISBN: 9783030816902
We consider an application of the AmgX library by NVIDIA as the preconditioner or solver for discrete elliptic problems expressed through Discontinuous Galerkin methods (DG) with various formulations. The effect of poor geometric multigrid performanc
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::737e97ed4b360545f03a1f4e554a6ec7
https://doi.org/10.1007/978-3-030-81691-9_13
https://doi.org/10.1007/978-3-030-81691-9_13
Autor:
N. M. Evstigneev
Publikováno v:
Communications in Computer and Information Science ISBN: 9783030816902
We consider a nonlinear autonomous large-scale dynamical system with a parameter. Such systems usually stem from the discretization of initial boundary value problems for nonlinear partial differential equations. We are interested in finding all peri
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5c6c7ea0b8ae71ff26e1f2cdbbf2b791
https://doi.org/10.1007/978-3-030-81691-9_6
https://doi.org/10.1007/978-3-030-81691-9_6
Autor:
N. M. Evstigneev, O. I. Ryabkov
Publikováno v:
Communications in Computer and Information Science ISBN: 9783030553258
Taylor Models present the polynomial generalization of the simple interval approach for rigorous computations of differential equations suggested by Martin Berz. These models are used to obtain better estimates for guaranteed enclosures of solutions.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::942a4ee0171b739383cd555c65fb3af9
https://doi.org/10.1007/978-3-030-55326-5_7
https://doi.org/10.1007/978-3-030-55326-5_7