Unified Transform for Boundary Value Problems: Applications and Advances

Beatrice Pelloni and Anthanasios S. Fokas

Published by Society for Industrial and Applied Mathematic, 2015
ISBN 10: 1611973813 / ISBN 13: 9781611973815
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Synopsis: 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.

Audience: This book is intended for applied and numerical research mathematicians and scientists working on the solution of boundary value problems in physics and engineering.

Contents: Chapter 1: Introduction; Part I: Theoretical Results; Chapter 2: Evolution Problems: Linear; Chapter 3: Evolution Problems: Nonlinear; Chapter 4: Elliptic Problems: Linear; Chapter 5: Elliptic Problems: Nonlinear; Part II: Between Theory and Applications; Chapter 6: Overview of Variational Formulations for Linear Elliptic PDEs; Part III: Applications; Chapter 7: Numerical Methods for Elliptic Problems; Chapter 8: Numerical Methods for Evolution Problems.

Book Description: This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. It is intended for applied and numerical research mathematicians and scientists working on the solution of boundary value problems in physics and engineering.

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Title: Unified Transform for Boundary Value ...
Publisher: Society for Industrial and Applied Mathematic
Publication Date: 2015
Binding: Trade Paperback
Book Condition: Very Good

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Book Description Society for Industrial & Applied Mathematics,U.S., United States, 2016. Paperback. Condition: New. Language: English. Brand new Book. 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 and discuss recent applications of the unified transform to the analysis and numerical modelling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method. The text covers a variety of aspects of the topic, including new theoretical results on linear and nonlinear evolutionary and elliptic problems, variational formulations for elliptic problems, and recent numerical applications based on the boundary element method and on the unified transform. The book is intended for applied and numerical research mathematicians and scientists working on the solution of boundary value problems in physics and engineering. Seller Inventory # AAN9781611973815

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Book Description Society for Industrial & Applied Mathematics,U.S., United States, 2016. Paperback. Condition: New. Language: English. Brand new Book. 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 and discuss recent applications of the unified transform to the analysis and numerical modelling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method. The text covers a variety of aspects of the topic, including new theoretical results on linear and nonlinear evolutionary and elliptic problems, variational formulations for elliptic problems, and recent numerical applications based on the boundary element method and on the unified transform. The book is intended for applied and numerical research mathematicians and scientists working on the solution of boundary value problems in physics and engineering. Seller Inventory # AAN9781611973815

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