Navier–Stokes Equations on R3 × [0, T]

Nonfiction, Science & Nature, Mathematics, Differential Equations
Cover of the book Navier–Stokes Equations on R3 × [0, T] by Frank Stenger, Don Tucker, Gerd Baumann, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Frank Stenger, Don Tucker, Gerd Baumann ISBN: 9783319275260
Publisher: Springer International Publishing Publication: September 23, 2016
Imprint: Springer Language: English
Author: Frank Stenger, Don Tucker, Gerd Baumann
ISBN: 9783319275260
Publisher: Springer International Publishing
Publication: September 23, 2016
Imprint: Springer
Language: English

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) ∈ 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 ∩ 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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) ∈ 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:

Following the proofs of denseness, the authors prove the existence of a solution of the integral equations in the space of functions A ∩ 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.

More books from Springer International Publishing

Cover of the book Frontiers and Progress in Multiphase Flow I by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book Doctoral Education for the Knowledge Society by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book International Digital Imaging Correlation Society by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book Simulation Based Engineering in Fluid Flow Design by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book Robot Operating System (ROS) by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book The Philosophy and Politics of Aesthetic Experience by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book Multimedia Services in Intelligent Environments by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book Cyber Resilience of Systems and Networks by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book Rule of Law, Human Rights and Judicial Control of Power by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book Advances in Human Factors in Wearable Technologies and Game Design by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book Electrochemistry in a Divided World by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book Geology of Coal Deposits of South Limburg, The Netherlands by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book Plant Responses to Hyperarid Desert Environments by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book Return Migration to Afghanistan by Frank Stenger, Don Tucker, Gerd Baumann
Cover of the book Linked Innovation by Frank Stenger, Don Tucker, Gerd Baumann
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy