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Více informací o knize Navier-Stokes Equations on R3 x [0, T]

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Anotace knihy

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.

Parametry knihy

Zařazení knihy Knihy v angličtině Mathematics & science Mathematics Calculus & mathematical analysis

• Plný název: Navier-Stokes Equations on R3 x [0, T]
• Autor: FRANK STENGER
• Jazyk: Angličtina
• Vazba: Brožovaná
• Počet stran: 226
• EAN: 9783319801629
• ISBN: 9783319801629
• ID: 19755551
• Nakladatelství: Springer International Publishing AG
• Hmotnost: 454 g
• Rozměry: 235 × 155 × 13 mm
• Datum vydání: 14. June 2018

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