Navier-Stokes Equations on R3 x [0, T] (Hardcover, 1st ed. 2016)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Release date:	October 2016
First published:	2016
Authors:	Frank Stenger • Don Tucker • Gerd Baumann
Dimensions:	235 x 155 x 14mm (L x W x T)
Format:	Hardcover
Pages:	226
Edition:	1st ed. 2016
ISBN-13:	978-3-319-27524-6
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Promotions
LSN:	3-319-27524-0
Barcode:	9783319275246

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