Author: I D Iliev
Publisher: CRC Press
ISBN: 9780582239630
Category : Mathematics
Languages : en
Pages : 412
Book Description
Soliton theory as a method for solving some classes of nonlinear evolution equations (soliton equations) is one of the most actively developing topics in mathematical physics. This book presents some spectral theory methods for the investigation of soliton equations ad the inverse scattering problems related to these equations. The authors give the theory of expansions for the Sturm-Liouville operator and the Dirac operator. On this basis, the spectral theory of recursion operators generating Korteweg-de Vries type equations is presented and the Ablowitz-Kaup-Newell-Segur scheme, through which the inverse scattering method could be understood as a Fourier-type transformation, is considered. Following these ideas, the authors investigate some of the questions related to inverse spectral problems, i.e. uniqueness theorems, construction of explicit solutions and approximative methods for solving inverse scattering problems. A rigorous investigation of the stability of soliton solutions including solitary waves for equations which do not allow integration within inverse scattering method is also presented.
Spectral Methods in Soliton Equations
Spectral Methods in Soliton Equations
Author: I. D. Iliev
Publisher: Halsted Press
ISBN: 9780470234778
Category : Mathematics
Languages : en
Pages : 384
Book Description
Publisher: Halsted Press
ISBN: 9780470234778
Category : Mathematics
Languages : en
Pages : 384
Book Description
Spectral Methods
Author: Claudio Canuto
Publisher: Springer Science & Business Media
ISBN: 3540307265
Category : Science
Languages : en
Pages : 585
Book Description
Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.
Publisher: Springer Science & Business Media
ISBN: 3540307265
Category : Science
Languages : en
Pages : 585
Book Description
Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.
Algebraic and Spectral Methods for Nonlinear Wave Equations
Author: Naruyoshi Asano
Publisher: Longman Scientific and Technical
ISBN:
Category : Mathematics
Languages : en
Pages : 448
Book Description
Publisher: Longman Scientific and Technical
ISBN:
Category : Mathematics
Languages : en
Pages : 448
Book Description
Solitons In Multidimensions: Inverse Spectral Transform Method
Author: B G Konopelchenko
Publisher: World Scientific
ISBN: 9814518069
Category :
Languages : en
Pages : 304
Book Description
The book is devoted to the mathematical theory of soliton phenomena on the plane. The inverse spectral transform method which is a main tool for the study of the (2+1)-dimensional soliton equation is reviewed. The ∂-problem and the Riemann-Hilbert problem method are discussed. Several basic examples of soliton equations are considered in detail. This volume is addressed both to the nonexpert and to the researcher in the field. This is the first literature dealing specifically with multidimensional solition equations.
Publisher: World Scientific
ISBN: 9814518069
Category :
Languages : en
Pages : 304
Book Description
The book is devoted to the mathematical theory of soliton phenomena on the plane. The inverse spectral transform method which is a main tool for the study of the (2+1)-dimensional soliton equation is reviewed. The ∂-problem and the Riemann-Hilbert problem method are discussed. Several basic examples of soliton equations are considered in detail. This volume is addressed both to the nonexpert and to the researcher in the field. This is the first literature dealing specifically with multidimensional solition equations.
Spectral Methods And Their Applications
Author: Ben-yu Guo
Publisher: World Scientific
ISBN: 9814496642
Category : Mathematics
Languages : en
Pages : 359
Book Description
This book presents the basic algorithms, the main theoretical results, and some applications of spectral methods. Particular attention is paid to the applications of spectral methods to nonlinear problems arising in fluid dynamics, quantum mechanics, weather prediction, heat conduction and other fields.The book consists of three parts. The first part deals with orthogonal approximations in Sobolev spaces and the stability and convergence of approximations for nonlinear problems, as the mathematical foundation of spectral methods. In the second part, various spectral methods are described, with some applications. It includes Fourier spectral method, Legendre spectral method, Chebyshev spectral method, spectral penalty method, spectral vanishing viscosity method, spectral approximation of isolated solutions, multi-dimensional spectral method, spectral method for high-order equations, spectral-domain decomposition method and spectral multigrid method. The third part is devoted to some recent developments of spectral methods, such as mixed spectral methods, combined spectral methods and spectral methods on the surface.
Publisher: World Scientific
ISBN: 9814496642
Category : Mathematics
Languages : en
Pages : 359
Book Description
This book presents the basic algorithms, the main theoretical results, and some applications of spectral methods. Particular attention is paid to the applications of spectral methods to nonlinear problems arising in fluid dynamics, quantum mechanics, weather prediction, heat conduction and other fields.The book consists of three parts. The first part deals with orthogonal approximations in Sobolev spaces and the stability and convergence of approximations for nonlinear problems, as the mathematical foundation of spectral methods. In the second part, various spectral methods are described, with some applications. It includes Fourier spectral method, Legendre spectral method, Chebyshev spectral method, spectral penalty method, spectral vanishing viscosity method, spectral approximation of isolated solutions, multi-dimensional spectral method, spectral method for high-order equations, spectral-domain decomposition method and spectral multigrid method. The third part is devoted to some recent developments of spectral methods, such as mixed spectral methods, combined spectral methods and spectral methods on the surface.
Spectral Transform and Solitons
Author: F. Calogero
Publisher: Elsevier
ISBN: 0080875343
Category : Mathematics
Languages : en
Pages : 533
Book Description
Spectral Transform and Solitons
Publisher: Elsevier
ISBN: 0080875343
Category : Mathematics
Languages : en
Pages : 533
Book Description
Spectral Transform and Solitons
Spectral Methods
Author: Jie Shen
Publisher: Springer Science & Business Media
ISBN: 3540710418
Category : Mathematics
Languages : en
Pages : 481
Book Description
Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.
Publisher: Springer Science & Business Media
ISBN: 3540710418
Category : Mathematics
Languages : en
Pages : 481
Book Description
Along with finite differences and finite elements, spectral methods are one of the three main methodologies for solving partial differential equations on computers. This book provides a detailed presentation of basic spectral algorithms, as well as a systematical presentation of basic convergence theory and error analysis for spectral methods. Readers of this book will be exposed to a unified framework for designing and analyzing spectral algorithms for a variety of problems, including in particular high-order differential equations and problems in unbounded domains. The book contains a large number of figures which are designed to illustrate various concepts stressed in the book. A set of basic matlab codes has been made available online to help the readers to develop their own spectral codes for their specific applications.
Spectral Elements for Transport-Dominated Equations
Author: Daniele Funaro
Publisher: Springer Science & Business Media
ISBN: 9783540626497
Category : Language Arts & Disciplines
Languages : en
Pages : 228
Book Description
The book deals with the numerical approximation of various PDEs using the spectral element method, with particular emphasis for elliptic equations dominated by first-order terms. It provides a simple introduction to spectral elements with additional new tools (upwind grids and preconditioners). Applications to fluid dynamics and semiconductor devices are considered, as well as in other models were transport-diffusion equations arise. The aim is to provide the reader with both introductive and more advanced material on spectral Legendre collocation methods. The book however does not cover all the aspects of spectral methods. Engineers, physicists and applied mathematicians may study how to implement the collocation method and use the results to improve their computational codes.
Publisher: Springer Science & Business Media
ISBN: 9783540626497
Category : Language Arts & Disciplines
Languages : en
Pages : 228
Book Description
The book deals with the numerical approximation of various PDEs using the spectral element method, with particular emphasis for elliptic equations dominated by first-order terms. It provides a simple introduction to spectral elements with additional new tools (upwind grids and preconditioners). Applications to fluid dynamics and semiconductor devices are considered, as well as in other models were transport-diffusion equations arise. The aim is to provide the reader with both introductive and more advanced material on spectral Legendre collocation methods. The book however does not cover all the aspects of spectral methods. Engineers, physicists and applied mathematicians may study how to implement the collocation method and use the results to improve their computational codes.
Spectral Methods
Author: Claudio Canuto
Publisher: Springer Science & Business Media
ISBN: 3540307281
Category : Mathematics
Languages : en
Pages : 616
Book Description
Following up the seminal Spectral Methods in Fluid Dynamics, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries. These types of spectral methods were only just emerging at the time the earlier book was published. The discussion of spectral algorithms for linear and nonlinear fluid dynamics stability analyses is greatly expanded. The chapter on spectral algorithms for incompressible flow focuses on algorithms that have proven most useful in practice, has much greater coverage of algorithms for two or more non-periodic directions, and shows how to treat outflow boundaries. Material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting. This book is a companion to Spectral Methods: Fundamentals in Single Domains.
Publisher: Springer Science & Business Media
ISBN: 3540307281
Category : Mathematics
Languages : en
Pages : 616
Book Description
Following up the seminal Spectral Methods in Fluid Dynamics, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries. These types of spectral methods were only just emerging at the time the earlier book was published. The discussion of spectral algorithms for linear and nonlinear fluid dynamics stability analyses is greatly expanded. The chapter on spectral algorithms for incompressible flow focuses on algorithms that have proven most useful in practice, has much greater coverage of algorithms for two or more non-periodic directions, and shows how to treat outflow boundaries. Material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting. This book is a companion to Spectral Methods: Fundamentals in Single Domains.