NAVIER-STOKES EQUATIONS ON R3 X (O,T) by Frank Stenger, Don Tucker, Gerd Baumann ( 9783319275246 )

Item Details

Title:

NAVIER-STOKES EQUATIONS ON R3 X (O,T)

Volume:

2016

By:

Frank Stenger, Don Tucker, Gerd Baumann

Format:

Hardback

List price:	£79.99
We currently do not stock this item, please contact the publisher directly for further information.

ISBN 10:

3319275240

ISBN 13:

9783319275246

Publisher:

SPRINGER INTERNATIONAL PUBLISHING AG

Pub. date:

24 September, 2016

Pages:

236

Synopsis:

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 x [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 x [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.

Illustrations:

25 colour illustrations, 1 black & white tables, biography

Publication:

Switzerland

Imprint:

Springer International Publishing AG

Returns:

Returnable

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