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Navier-Stokes Equations on R3 × [0, T]
In this monograph, leading researchers in the world of numerical analysis, partial differential equations, and hard computational problems study the properties of solutions of the Navier-Stokes partial differential equations on (x, y, z, t) ∈ ℝ3 × [0, T]. Initially converting the PDE to a system of...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2016.
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| Edición: | 1st ed. 2016. |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
| LEADER | 00000nam a22000005i 4500 | ||
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| 001 | 978-3-319-27526-0 | ||
| 003 | DE-He213 | ||
| 005 | 20220203105814.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 160923s2016 sz | s |||| 0|eng d | ||
| 020 | |a 9783319275260 |9 978-3-319-27526-0 | ||
| 024 | 7 | |a 10.1007/978-3-319-27526-0 |2 doi | |
| 050 | 4 | |a QA370-380 | |
| 072 | 7 | |a PBKJ |2 bicssc | |
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| 072 | 7 | |a PBKJ |2 thema | |
| 082 | 0 | 4 | |a 515.35 |2 23 |
| 100 | 1 | |a Stenger, Frank. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Navier-Stokes Equations on R3 × [0, T] |h [electronic resource] / |c by Frank Stenger, Don Tucker, Gerd Baumann. |
| 250 | |a 1st ed. 2016. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2016. | |
| 300 | |a X, 226 p. 25 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 505 | 0 | |a Preface -- Introduction, PDE, and IE Formulations -- Spaces of Analytic Functions -- Spaces of Solution of the N-S Equations -- Proof of Convergence of Iteration 1.6.3 -- Numerical Methods for Solving N-S Equations -- Sinc Convolution Examples -- Implementation Notes -- Result Notes. | |
| 520 | |a In this monograph, leading researchers in the world of numerical analysis, partial differential equations, and hard computational problems study the properties of solutions of the Navier-Stokes partial differential equations on (x, y, z, t) ∈ ℝ3 × [0, T]. Initially converting the PDE to a system of integral equations, the authors then describe spaces A of analytic functions that house solutions of this equation, and show that these spaces of analytic functions are dense in the spaces S of rapidly decreasing and infinitely differentiable functions. This method benefits from the following advantages: The functions of S are nearly always conceptual rather than explicit Initial and boundary conditions of solutions of PDE are usually drawn from the applied sciences, and as such, they are nearly always piece-wise analytic, and in this case, the solutions have the same properties When methods of approximation are applied to functions of A they converge at an exponential rate, whereas methods of approximation applied to the functions of S converge only at a polynomial rate Enables sharper bounds on the solution enabling easier existence proofs, and a more accurate and more efficient method of solution, including accurate error bounds Following the proofs of denseness, the authors prove the existence of a solution of the integral equations in the space of functions A ∩ ℝ3 × [0, T], and provide an explicit novel algorithm based on Sinc approximation and Picard-like iteration for computing the solution. Additionally, the authors include appendices that provide a custom Mathematica program for computing solutions based on the explicit algorithmic approximation procedure, and which supply explicit illustrations of these computed solutions. | ||
| 650 | 0 | |a Differential equations. | |
| 650 | 1 | 4 | |a Differential Equations. |
| 700 | 1 | |a Tucker, Don. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Baumann, Gerd. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783319275246 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319275253 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319801629 |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-27526-0 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||