Perturbation Of The Boundary In Boundary Value Problems Of Partial Differential Equations
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| Author | : Dan Henry |
| Publisher | : Cambridge University Press |
| Total Pages | : 220 |
| Release | : 2005-05-26 |
| Genre | : Mathematics |
| ISBN | : 9781139441179 |
Perturbation of the boundary is a rather neglected topic in the study of partial differential equations, in part because it often entails long and difficult caluclations. In this book, first published in 2005, the author carefully discusses a calculus that overcomes the computational morass, and he goes on to develop more general forms of standard theorems, helping to answer a problems involving boundary perturbations.
| Author | : Ferdinand Verhulst |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 332 |
| Release | : 2006-06-04 |
| Genre | : Mathematics |
| ISBN | : 0387283137 |
Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
| Author | : N. E. Tovmasyan |
| Publisher | : World Scientific |
| Total Pages | : 252 |
| Release | : 1994 |
| Genre | : Science |
| ISBN | : 9789810213510 |
The book is devoted to boundary value problems for general partial differential equations. Efficient methods of resolution of boundary value problems for elliptic equations, based on the theory of analytic functions and having great theoretical and practical importance are developed.A new approach to the investigation of electromagnetic fields is sketched, permitting laws of propagation of electromagnetic energy at a great distance, is outlined and asymptotic formulae for solutions of Maxwell's equation is obtained. These equations are also applied to the efficient resolution of problems.The book is based mostly on the investigation of the author, a considerable part of which being published for the first time.
| Author | : Allaberen Ashyralyev |
| Publisher | : Birkhäuser |
| Total Pages | : 453 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034879229 |
This book explores new difference schemes for approximating the solutions of regular and singular perturbation boundary-value problems for PDEs. The construction is based on the exact difference scheme and Taylor's decomposition on the two or three points, which permits investigation of differential equations with variable coefficients and regular and singular perturbation boundary value problems.
| Author | : Hans-Görg Roos |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 599 |
| Release | : 2008-09-17 |
| Genre | : Mathematics |
| ISBN | : 3540344675 |
This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
| Author | : Gung-Min Gie |
| Publisher | : Springer |
| Total Pages | : 424 |
| Release | : 2018-11-21 |
| Genre | : Mathematics |
| ISBN | : 3030006387 |
Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane, or the flow of air around a car. Also in many instances in geophysical fluid mechanics, like the interface of air and earth, or air and ocean. This self-contained monograph is devoted to the study of certain classes of singular perturbation problems mostly related to thermic, fluid mechanics and optics and where mostly elliptic or parabolic equations in a bounded domain are considered. This book is a fairly unique resource regarding the rigorous mathematical treatment of boundary layer problems. The explicit methodology developed in this book extends in many different directions the concept of correctors initially introduced by J. L. Lions, and in particular the lower- and higher-order error estimates of asymptotic expansions are obtained in the setting of functional analysis. The review of differential geometry and treatment of boundary layers in a curved domain is an additional strength of this book. In the context of fluid mechanics, the outstanding open problem of the vanishing viscosity limit of the Navier-Stokes equations is investigated in this book and solved for a number of particular, but physically relevant cases. This book will serve as a unique resource for those studying singular perturbations and boundary layer problems at the advanced graduate level in mathematics or applied mathematics and may be useful for practitioners in other related fields in science and engineering such as aerodynamics, fluid mechanics, geophysical fluid mechanics, acoustics and optics.
| Author | : Bhimsen Shivamoggi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 374 |
| Release | : 2002-12-13 |
| Genre | : Mathematics |
| ISBN | : 9780817641894 |
Perturbation methods are widely used in the study of physically significant differential equations, which arise in Applied Mathematics, Physics and Engineering.; Background material is provided in each chapter along with illustrative examples, problems, and solutions.; A comprehensive bibliography and index complete the work.; Covers an important field of solutions for engineering and the physical sciences.; To allow an interdisciplinary readership, the book focuses almost exclusively on the procedures and the underlying ideas and soft pedal the proofs; Dr. Bhimsen K. Shivamoggi has authored seven successful books for various publishers like John Wiley & Sons and Kluwer Academic Publishers.
| Author | : Ravi P. Agarwal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 422 |
| Release | : 2008-11-13 |
| Genre | : Mathematics |
| ISBN | : 0387791469 |
In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice. The treatment of ODEs is developed in conjunction with PDEs and is aimed mainly towards applications. The book covers important applications-oriented topics such as solutions of ODEs in form of power series, special functions, Bessel functions, hypergeometric functions, orthogonal functions and polynomials, Legendre, Chebyshev, Hermite, and Laguerre polynomials, theory of Fourier series. Undergraduate and graduate students in mathematics, physics and engineering will benefit from this book. The book assumes familiarity with calculus.
| Author | : C. De Coster |
| Publisher | : Elsevier |
| Total Pages | : 502 |
| Release | : 2006-03-21 |
| Genre | : Mathematics |
| ISBN | : 0080462472 |
This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction.· Presents the fundamental features of the method· Construction of lower and upper solutions in problems· Working applications and illustrated theorems by examples· Description of the history of the method and Bibliographical notes
| Author | : Uri M. Ascher |
| Publisher | : SIAM |
| Total Pages | : 620 |
| Release | : 1994-12-01 |
| Genre | : Mathematics |
| ISBN | : 9781611971231 |
This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
