|
|
|
Navier–Stokes Equations on R3 × [0, T]
|
(Buch) |
Dieser Artikel gilt, aufgrund seiner Grösse, beim Versand als 3 Artikel!
| Inhalt: |
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 × [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 × [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. |
|
Auf Bestellung (Lieferzeit unbekannt)
Newsfeed | 
Facebook | 
Twitter
