Author: A. M. Ilʹin A. M. Il'inPublisher: American Mathematical Soc.
ISBN: 9780821897348
Category : Asymptotic expansions
Languages : en
Pages : 754
Book Description
Matching of Asymptotic Expansions of Solutions of Boundary Value Problems
Author: A. M. Ilʹin A. M. Il'inPublisher: American Mathematical Soc.
ISBN: 9780821897348
Category : Asymptotic expansions
Languages : en
Pages : 754
Book Description
Partial Differential Equations V
Author: M.V. FedoryukPublisher: Springer Science & Business Media
ISBN: 9783540533719
Category : Mathematics
Languages : en
Pages : 262
Book Description
The six articles in this EMS volume provide an overview of a number of mid-to-late-1990s techniques in the study of the asymptotic behaviour of partial differential equations. These techniques include the Maslov canonical operator, and semiclassical asymptotics of solutions and eigenfunctions.
Advanced Mathematical Methods for Scientists and Engineers I
Author: Carl M. BenderPublisher: Springer Science & Business Media
ISBN: 1475730691
Category : Mathematics
Languages : en
Pages : 605
Book Description
A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
Asymptotic Analysis and Boundary Layers
Author: Jean CousteixPublisher: Springer Science & Business Media
ISBN: 3540464891
Category : Science
Languages : en
Pages : 437
Book Description
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.
Historical Developments in Singular Perturbations
Author: Robert E. O'MalleyPublisher: Springer
ISBN: 3319119249
Category : Mathematics
Languages : en
Pages : 263
Book Description
This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.
Matched Asymptotic Expansions in Reaction-Diffusion Theory
Author: J.A. LeachPublisher: Springer Science & Business Media
ISBN: 0857293966
Category : Mathematics
Languages : en
Pages : 289
Book Description
This volume contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory. It can be viewed both as a handbook, and as a detailed description of the methodology. The authors present new methods based on matched asymptotic expansions.
Perturbation Methods
Author: E. J. HinchPublisher: Cambridge University Press
ISBN: 9780521378970
Category : Mathematics
Languages : en
Pages : 178
Book Description
A textbook presenting the theory and underlying techniques of perturbation methods in a manner suitable for senior undergraduates from a broad range of disciplines.
Analytic Functions of Several Complex Variables
Author: Robert Clifford GunningPublisher: American Mathematical Soc.
ISBN: 0821821652
Category : Mathematics
Languages : en
Pages : 338
Book Description
The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century. This title intends to provide an extensive introduction to the Oka-Cartan theory and some of its applications, and to the general theory of analytic spaces.
Perturbation Methods in Applied Mathematics
Author: J. KevorkianPublisher: Springer Science & Business Media
ISBN: 1475742134
Category : Mathematics
Languages : en
Pages : 569
Book Description
This book is a revised and updated version, including a substantial portion of new material, of J. D. Cole's text Perturbation Methods in Applied Mathe matics, Ginn-Blaisdell, 1968. We present the material at a level which assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate level course on the subject. The applied mathematician, attempting to understand or solve a physical problem, very often uses a perturbation procedure. In doing this, he usually draws on a backlog of experience gained from the solution of similar examples rather than on some general theory of perturbations. The aim of this book is to survey these perturbation methods, especially in connection with differ ential equations, in order to illustrate certain general features common to many examples. The basic ideas, however, are also applicable to integral equations, integrodifferential equations, and even to_difference equations. In essence, a perturbation procedure consists of constructing the solution for a problem involving a small parameter B, either in the differential equation or the boundary conditions or both, when the solution for the limiting case B = 0 is known. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of B.
Around the Research of Vladimir Maz'ya II
Author: Ari LaptevPublisher: Springer Science & Business Media
ISBN: 1441913432
Category : Mathematics
Languages : en
Pages : 404
Book Description
Topics of this volume are close to scientific interests of Professor Maz'ya and use, directly or indirectly, the fundamental influential Maz'ya's works penetrating, in a sense, the theory of PDEs. In particular, recent advantages in the study of semilinear elliptic equations, stationary Navier-Stokes equations, the Stokes system in convex polyhedra, periodic scattering problems, problems with perturbed boundary at a conic point, singular perturbations arising in elliptic shells and other important problems in mathematical physics are presented.