Navier-Stokes Equations on R3 × [0, T] (PDF)
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,...
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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-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 n 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.
- Autoren: Frank Stenger , Don Tucker , Gerd Baumann
- 2016, 1st ed. 2016, 226 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319275267
- ISBN-13: 9783319275260
- Erscheinungsdatum: 23.09.2016
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