Produktbild: Navier-Stokes Equations on R3 × [0, T]

Navier-Stokes Equations on R3 × [0, T]

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106,99 €

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ISBN: 3319801627
ISBN 13: 9783319801629
Autor: Stenger, Frank/Tucker, Don/Baumann, Gerd
Verlag: Springer Verlag GmbH
Umfang: x, 226 S., 25 farbige Illustr., 226 p. 25 illus. in color.
Erscheinungsdatum: 14.06.2018
Auflage: 1/2016
Produktform: Kartoniert
Einband: Kartoniert

Studies the properties of solutionsof the Navier-Stokes partial differential equations on (x, y, z, t) ? R3 × [0, T]Demonstrates a new method fordetermining solutions of the Navier-Stokes equations by converting partialdifferential equations to a system of integral equations describing spaces ofanalytic functions containing solutionsEnables sharper bounds on solutions to NavierStokes equations, easier existence proofs, and a more accurate, efficient method of determining a solution with accurate error boundsIncludes an custom-written Mathematica package for computing solutions to the Navier-Stokes equations based on the author’s approximation methodIncludes supplementary material: sn.pub/extras

Artikelnummer: 5448444 Kategorie:

Beschreibung

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) 3 × [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 3 × [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.

Herstellerkennzeichnung:


Springer Verlag GmbH
Tiergartenstr. 17
69121 Heidelberg
DE

E-Mail: juergen.hartmann@springer.com

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