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

Stenger, Frank; Tucker, Don; Baumann, Gerd

 
9783319275246: Navier–Stokes Equations on R3 × [0, T]
Hardcover
ISBN 10: 3319275240 ISBN 13: 9783319275246
Verlag: Springer, 2016

Inhaltsangabe

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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Von der hinteren Coverseite

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2016
Sprache
Englisch
ISBN 10 
3319275240
ISBN 13 
9783319275246
Einband
Gebundene Ausgabe
Auflage
1
Anzahl der Seiten
236
Kontakt zum Hersteller
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Deutschland

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Softcover