Pelloni, Beatrice
Overview
Works:  9 works in 20 publications in 1 language and 131 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Editor, Translator, Author 
Publication Timeline
.
Most widely held works by
Beatrice Pelloni
Unified transform for boundary value problems : applications and advances(
Book
)
6 editions published in 2015 in English and held by 101 WorldCat member libraries worldwide
This book describes stateoftheart 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 wellestablished 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. Novel 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.[Source inconnue]
6 editions published in 2015 in English and held by 101 WorldCat member libraries worldwide
This book describes stateoftheart 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 wellestablished 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. Novel 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.[Source inconnue]
Analytical mechanics : an introduction by
A Fasano(
Book
)
6 editions published between 2006 and 2013 in English and held by 20 WorldCat member libraries worldwide
Is the solar system stable? Is there a unifying 'economy' principle in mechanics? How can a pointmass be described as a 'wave'? This book offers students an understanding of the most relevant and far reaching results of the theory of Analytical Mechanics, including plenty of examples, exercises, and solved problems.  ;Analytical Mechanics is the investigation of motion with the rigorous tools of mathematics. Rooted in the works of Lagrange, Euler, Poincareacute; (to mention just a few), it is a very classical subject with fascinating developments and still rich of open problems. It addres
6 editions published between 2006 and 2013 in English and held by 20 WorldCat member libraries worldwide
Is the solar system stable? Is there a unifying 'economy' principle in mechanics? How can a pointmass be described as a 'wave'? This book offers students an understanding of the most relevant and far reaching results of the theory of Analytical Mechanics, including plenty of examples, exercises, and solved problems.  ;Analytical Mechanics is the investigation of motion with the rigorous tools of mathematics. Rooted in the works of Lagrange, Euler, Poincareacute; (to mention just a few), it is a very classical subject with fascinating developments and still rich of open problems. It addres
Proceedings of the 13th Workshop NEEDS'99 : Nonlinear evolution equations and dynamical systems, Crete (Greece), June 20July
30, 1999 by Workshop on Nonlinear Evolution Equations and Dynamical Systems(
Book
)
1 edition published in 2001 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 3 WorldCat member libraries worldwide
Nonlinear evolution equations and dynamical systems by
Sandra Carillo(
Book
)
2 editions published in 2001 in English and held by 2 WorldCat member libraries worldwide
Nonlinear Evolution Equations and Dynamical Systems (NEEDS) provides a presentation of the state of the art. Except for a few review papers, the 40 contributions are intentially brief to give only the gist of the methods, proofs, etc. including references to the relevant litera ture. This gives a handy overview of current research activities. Hence, the book should be equally useful to the senior resercher as well as the colleague just entering the field. Keypoints treated are: i) integrable systems in multidimensions and associated phenomenology ("dromions"); ii) criteria and tests of integrability (e.g., Painlev test); iii) new developments related to the scattering transform; iv) algebraic approaches to integrable systems and Hamiltonian theory (e.g., connections with YoungBaxter equations and KacMoody algebras); v) new developments in mappings and cellular automata, vi) applications to general relativity, condensed matter physics, and oceanography
2 editions published in 2001 in English and held by 2 WorldCat member libraries worldwide
Nonlinear Evolution Equations and Dynamical Systems (NEEDS) provides a presentation of the state of the art. Except for a few review papers, the 40 contributions are intentially brief to give only the gist of the methods, proofs, etc. including references to the relevant litera ture. This gives a handy overview of current research activities. Hence, the book should be equally useful to the senior resercher as well as the colleague just entering the field. Keypoints treated are: i) integrable systems in multidimensions and associated phenomenology ("dromions"); ii) criteria and tests of integrability (e.g., Painlev test); iii) new developments related to the scattering transform; iv) algebraic approaches to integrable systems and Hamiltonian theory (e.g., connections with YoungBaxter equations and KacMoody algebras); v) new developments in mappings and cellular automata, vi) applications to general relativity, condensed matter physics, and oceanography
Unified transform for boundary value problems : applications and advances by
A. S Fokas(
Book
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
This book describes stateoftheart 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 wellestablished 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. Novel 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
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
This book describes stateoftheart 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 wellestablished 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. Novel 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
Advances in the study of boundary value problems for nonlinear integrable PDEs(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
Abstract: In this review I summarize some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations (PDEs) in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the unified transform or Fokas transform, that provides a substantial generalization of the classical inverse scattering transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the inverse scattering transform follows the 'separation of variables' philosophy, albeit in a nonlinear setting, the unified transform is based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalization to certain nonlinear cases of particular significance
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
Abstract: In this review I summarize some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations (PDEs) in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the unified transform or Fokas transform, that provides a substantial generalization of the classical inverse scattering transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the inverse scattering transform follows the 'separation of variables' philosophy, albeit in a nonlinear setting, the unified transform is based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalization to certain nonlinear cases of particular significance
Nonlinear evolution equations and dynamical systems : proceedings of the 13th Workshop NEEDS '99, Crete, Greece, 2030 june
1999. Ed.by Beatrice Pelloni(
Book
)
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
1 edition published in 2001 in English and held by 1 WorldCat member library worldwide
A numerical implementation of the unified Fokas transform for evolution problems on a finite interval(
)
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Abstract : We present the numerical solution of twopoint boundary value problems for a thirdorder linear PDE, representing a linear evolution in one space dimension. To our knowledge, the numerical evaluation of the solution so far could only be obtained by a timestepping scheme, that must also take into account the issue, generically nontrivial, of the imposition of the boundary conditions. Instead of computing the evolution numerically, we evaluate the novel solution representation formula obtained by the unified transform, also known as Fokas transform. This representation involves complex line integrals, but in order to evaluate these integrals numerically, it is necessary to deform the integration contours using appropriate deformation mappings. We formulate a strategy to implement effectively this deformation, which allows us to obtain accurate numerical results
1 edition published in 2017 in English and held by 1 WorldCat member library worldwide
Abstract : We present the numerical solution of twopoint boundary value problems for a thirdorder linear PDE, representing a linear evolution in one space dimension. To our knowledge, the numerical evaluation of the solution so far could only be obtained by a timestepping scheme, that must also take into account the issue, generically nontrivial, of the imposition of the boundary conditions. Instead of computing the evolution numerically, we evaluate the novel solution representation formula obtained by the unified transform, also known as Fokas transform. This representation involves complex line integrals, but in order to evaluate these integrals numerically, it is necessary to deform the integration contours using appropriate deformation mappings. We formulate a strategy to implement effectively this deformation, which allows us to obtain accurate numerical results
Spectral methods for the numerical solution of nonlinear dispersive wave equations by
Beatrice Pelloni(
)
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
1 edition published in 1996 in English and held by 1 WorldCat member library worldwide
Audience Level
0 

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Related Identities
 Fokas, A. S. 1952 Author Editor
 Society for Industrial and Applied Mathematics Publisher
 Marmi, S. (Stefano) 1963
 Fasano, A. (Antonio) Author
 Bruschi, Mario Editor
 Ragnisco, O. (Orlando) 1946 Editor
 KESICI, EMINE
 PRYER, TRISTAN
 SMITH, DAVID