Unified Transform for Boundary Value Problems

Applications and Advances

Häftad, Engelska, 2014

AvBeatrice Pelloni,Anthanasios S. Fokas,A.S. Fokas,B. Pelloni

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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.

Produktinformation

Utgivningsdatum2014-12-30
Mått152 x 229 x 16 mm
Vikt558 g
FormatHäftad
SpråkEngelska
Antal sidor304
FörlagSociety for Industrial & Applied Mathematics,U.S.
ISBN9781611973815

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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. 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.

Chapter 1: IntroductionPart I: Theoretical ResultsChapter 2: Evolution Problems: LinearChapter 3: Evolution Problems: NonlinearChapter 4: Elliptic Problems: LinearChapter 5: Elliptic Problems: NonlinearPart II: Between Theory and ApplicationsChapter 6: Overview of Variational Formulations for Linear Elliptic PDEsPart III: ApplicationsChapter 7: Numerical Methods for Elliptic ProblemsChapter 8: Numerical Methods for Evolution Problems.