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Navier–Stokes Equations on R3 × [0, T] / Frank Stenger, Don Tucker, Gerd Baumann | |
Publisher: Springer | |
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Sales Rank: 7185583 | |
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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 Stokespartial 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:
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.