Books in Partial differential equations

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Nonlinear Partial Differential Equations in Applied Science

• 1st Edition
• Volume 81
• April 1, 2000
• H. Fujita + 2 more
• English
• eBook 978-0-08-087192-9

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Differential Equations

• 1st Edition
• Volume 92
• April 1, 2000
• I.W. Knowles + 1 more
• English
• eBook 978-0-08-087203-2

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This volume forms a record of the lectures given at this International Conference. Under the general heading of the equations of mathematical physics, contributions are included on a broad range of topics in the theory and applications of ordinary and partial differential equations, including both linear and non-linear equations. The topics cover a wide variety of methods (spectral, theoretical, variational, topological, semi-group), and a equally wide variety of equations including the Laplace equation, Navier-Stokes equations, Boltzmann's equation, reaction-diffusion equations, Schroedinger equations and certain non-linear wave equations. A number of papers are devoted to multi-particle scattering theory, and to inverse theory. In addition, many of the plenary lectures contain a significant amount of survey material on a wide variety of these topics.

Recent Topics in Nonlinear PDE

• 1st Edition
• Volume 98
• April 1, 2000
• M. Mimura + 1 more
• English
• eBook 978-0-08-087209-4

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This volume contains papers covering the theory of nonlinear PDEs and the related topics which have been recently developed in Japan.

Recent Topics in Nonlinear PDE IV

• 1st Edition
• Volume 160
• April 1, 2000
• M. Mimura + 1 more
• English
• eBook 978-0-08-088020-4

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This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.

Computer Solution of Large Linear Systems

• 1st Edition
• Volume 28
• June 16, 1999
• Gerard Meurant
• English
• eBook 978-0-08-052951-6

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This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.

Fractional Differential Equations

• 1st Edition
• Volume 198
• October 21, 1998
• Igor Podlubny
• English
• Hardback 978-0-12-558840-9

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• eBook 978-0-08-053198-4

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This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'.This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models.In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications.

Multiscale Wavelet Methods for Partial Differential Equations

• 1st Edition
• Volume 6
• August 4, 1997
• Wolfgang Dahmen + 2 more
• English
• eBook 978-0-08-053714-6

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This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource.

The Theory of Singular Perturbations

• 1st Edition
• Volume 42
• November 8, 1996
• E.M. de Jager + 1 more
• English
• eBook 978-0-08-054275-1

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The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed.The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathematical justification of these methods. The latter implies a priori estimates of solutions of differential equations; this involves the application of Gronwall's lemma, maximum principles, energy integrals, fixed point theorems and Gåding's theorem for general elliptic equations. These features make the book of value to mathematicians and researchers in the engineering sciences, interested in the mathematical justification of formal approximations of solutions of practical perturbation problems. The text is selfcontained and each chapter is concluded with some exercises.

Handbook of Analysis and Its Foundations

• 1st Edition
• October 24, 1996
• Eric Schechter
• English
• eBook 978-0-08-053299-8

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Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook.

Algebraic and Analytic Methods in Representation Theory

• 1st Edition
• Volume 17
• September 27, 1996
• Bent Orsted
• English
• eBook 978-0-08-052695-9

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This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike.