Navier-Stokes Equations on R3 × [0, T]
Autor: | Frank Stenger, Don Tucker, Gerd Baumann |
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EAN: | 9783319275260 |
eBook Format: | |
Sprache: | Englisch |
Produktart: | eBook |
Veröffentlichungsdatum: | 23.09.2016 |
Kategorie: | |
Schlagworte: | Integral Equations Navier-Stokes Equations Numerical Methods for Solving Navier-Stokes Equations Partial Differential Equations Sinc Convolution Examples Spaces of Analytic Functions |
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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.