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A Unified Approach to Boundary Value Problems

2008-11-06 Mathematics
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Release : 2008-11-06
Genre : Mathematics
Kind : eBook
Book Rating : 519/5 ( reviews)

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Book Synopsis A Unified Approach to Boundary Value Problems by : Athanassios S. Fokas

Download or read book A Unified Approach to Boundary Value Problems written by Athanassios S. Fokas. This book was released on 2008-11-06. Available in PDF, EPUB and Kindle. Book excerpt: A novel approach to analysing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, based on ideas of the inverse scattering transform that the author introduced in 1997. This method is unique in also yielding novel integral representations for linear PDEs. Several new developments are addressed in the book, including a new transform method for linear evolution equations on the half-line and on the finite interval; analytical inversion of certain integrals such as the attenuated Radon transform and the Dirichlet-to-Neumann map for a moving boundary; integral representations for linear boundary value problems; analytical and numerical methods for elliptic PDEs in a convex polygon; and integrable nonlinear PDEs. An epilogue provides a list of problems on which the author's new approach has been used, offers open problems, and gives a glimpse into how the method might be applied to problems in three dimensions.

Unified Transform for Boundary Value Problems

2015-01-01 Mathematics
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Release : 2015-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 821/5 ( reviews)

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Book Synopsis Unified Transform for Boundary Value Problems by : Athanasios S. Fokas

Download or read book Unified Transform for Boundary Value Problems written by Athanasios S. Fokas. This book was released on 2015-01-01. Available in PDF, EPUB and Kindle. Book excerpt: This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs. The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.

A Unified Approach to Boundary Value Problems at Resonance with the First Eigenvalue

1996
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Release : 1996
Genre :
Kind : eBook
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Book Synopsis A Unified Approach to Boundary Value Problems at Resonance with the First Eigenvalue by : E. Serra

Download or read book A Unified Approach to Boundary Value Problems at Resonance with the First Eigenvalue written by E. Serra. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Solution of Two Point Boundary Value Problems

1976-01-01 Mathematics
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Release : 1976-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 449/5 ( reviews)

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Book Synopsis Numerical Solution of Two Point Boundary Value Problems by : Herbert B. Keller

Download or read book Numerical Solution of Two Point Boundary Value Problems written by Herbert B. Keller. This book was released on 1976-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.

Initial-boundary Value Problems and the Navier-Stokes Equations

1989-01-01 Science
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Release : 1989-01-01
Genre : Science
Kind : eBook
Book Rating : 135/5 ( reviews)

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Book Synopsis Initial-boundary Value Problems and the Navier-Stokes Equations by : Heinz-Otto Kreiss

Download or read book Initial-boundary Value Problems and the Navier-Stokes Equations written by Heinz-Otto Kreiss. This book was released on 1989-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This book provides an introduction to the vast subject of initial and initial-boundary value problems for PDEs, with an emphasis on applications to parabolic and hyperbolic systems. The Navier-Stokes equations for compressible and incompressible flows are taken as an example to illustrate the results. Researchers and graduate students in applied mathematics and engineering will find Initial-Boundary Value Problems and the Navier-Stokes Equations invaluable. The subjects addressed in the book, such as the well-posedness of initial-boundary value problems, are of frequent interest when PDEs are used in modeling or when they are solved numerically. The reader will learn what well-posedness or ill-posedness means and how it can be demonstrated for concrete problems. There are many new results, in particular on the Navier-Stokes equations. The direct approach to the subject still gives a valuable introduction to an important area of applied analysis.

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