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Unified Transform for Boundary Value Problems
Applications and Advances

£68.00

Authors:
Beatrice Pelloni, University of Reading
Anthanasios S. Fokas, University of Cambridge

A. S. Fokas, B. Pelloni, D. Mantzavinos, D. A. Smith, G. Biondini, D. Shepelsky, A. C. L. Ashton, E. A. Spence, A. Iserles, S. A. Smitheman, J. Lenells, S. N. Chandler-Wilde, S. Langdon, X. Claeys, R. Hiptmair, C. Jerez-Hanckes, S. Pintarelli, T. Trogdon

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Date Published: May 2015
availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
format: Paperback
isbn: 9781611973815

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Description

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About the Authors

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.
- Describes a novel and simple analytical method of unprecedented power for solving boundary value problems for linear PDEs
- Introduces simple techniques for the numerical solution of linear evolution and linear elliptic PDEs
- Reviews the state of the art on boundary element methods
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Product details
- Date Published: May 2015
- format: Paperback
- isbn: 9781611973815
- length: 320 pages
- dimensions: 254 x 174 x 16 mm
- weight: 0.55kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
Table of Contents
Preface
1. Introduction A. S. Fokas and B. Pelloni
Part I. Theoretical Results:
2. Evolution problems: linear D. Mantzavinos and D. A. Smith
3. Evolution problems: nonlinear G. Biondini, A. S. Fokas and D. Shepelsky
4. Elliptic problems: linear A. C. L. Ashton
5. Elliptic problems: nonlinear B. Pelloni
Part II. Between Theory and Applications:
6. Overview of variational formulations for linear elliptic PDEs E. A. Spence
Part III. Applications:
7. Numerical methods for elliptic problems A. S. Fokas, A. Iserles, S. A. Smitheman, J. Lenells, S. N. Chandler-Wilde, S. Langdon, X. Claeys, R. Hiptmair, C. Jerez-Hanckes and S. Pintarelli
8. Numerical methods for evolution problems T. Trogdon
Index.
Authors
Beatrice Pelloni, University of Reading
B. Pelloni is a Professor of Mathematics at the University of Reading. She has published over 30 papers on the unified transform and lectured on it as the Olga Taussky-Todd prize lecturer at ICIAM 2011. She is a fellow of the Institute for Mathematics and Its Applications and a member of the London Mathematical Society.
Anthanasios S. Fokas, University of Cambridge
A. S. Fokas is the Chair of Nonlinear Mathematical Science in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. Among his many awards are the Naylor Prize, the Excellence Prize of the Bodossaki Foundation, and a Guggenheim Fellowship. He is a member of the Academy of Athens and is included in the list of most highly cited researchers in mathematics. He is the originator of the unified transform.
Contributors
A. S. Fokas, B. Pelloni, D. Mantzavinos, D. A. Smith, G. Biondini, D. Shepelsky, A. C. L. Ashton, E. A. Spence, A. Iserles, S. A. Smitheman, J. Lenells, S. N. Chandler-Wilde, S. Langdon, X. Claeys, R. Hiptmair, C. Jerez-Hanckes, S. Pintarelli, T. Trogdon