Perturbation Methods in Fluid Mechanics
Author | : Milton Van Dyke |
Publisher | : |
Total Pages | : 252 |
Release | : 1964 |
Genre | : Fluid dynamics |
ISBN | : |
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Author | : Milton Van Dyke |
Publisher | : |
Total Pages | : 252 |
Release | : 1964 |
Genre | : Fluid dynamics |
ISBN | : |
Author | : Milton Van Dyke |
Publisher | : Parabolic Press, Incorporated |
Total Pages | : 296 |
Release | : 1975 |
Genre | : Science |
ISBN | : |
Author | : J. Kevorkian |
Publisher | : Springer Science & Business Media |
Total Pages | : 569 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475742134 |
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.
Author | : AlanW. Bush |
Publisher | : Routledge |
Total Pages | : 320 |
Release | : 2018-05-04 |
Genre | : Mathematics |
ISBN | : 1351425366 |
The subject of perturbation expansions is a powerful analytical technique which can be applied to problems which are too complex to have an exact solution, for example, calculating the drag of an aircraft in flight. These techniques can be used in place of complicated numerical solutions. This book provides an account of the main techniques of perturbation expansions applied to both differential equations and integral expressions. Features include a non-rigorous treatment of the subject at undergraduate level not available in any other current text; contains computer programs to enable the student to explore particular ideas and realistic case studies of industrial applications; a number of practical examples are included in the text to enhance understanding of points raised, particularly in the areas of mechanics and fluid mechanics; presents the main techniques of perturbation expansion at a level accessible to the undergraduate student.
Author | : E. J. Hinch |
Publisher | : Cambridge University Press |
Total Pages | : 178 |
Release | : 1991-10-25 |
Genre | : Mathematics |
ISBN | : 9780521378970 |
A textbook presenting the theory and underlying techniques of perturbation methods in a manner suitable for senior undergraduates from a broad range of disciplines.
Author | : AlanW. Bush |
Publisher | : Routledge |
Total Pages | : 185 |
Release | : 2018-05-04 |
Genre | : Mathematics |
ISBN | : 1351425358 |
The subject of perturbation expansions is a powerful analytical technique which can be applied to problems which are too complex to have an exact solution, for example, calculating the drag of an aircraft in flight. These techniques can be used in place of complicated numerical solutions. This book provides an account of the main techniques of perturbation expansions applied to both differential equations and integral expressions. Features include a non-rigorous treatment of the subject at undergraduate level not available in any other current text; contains computer programs to enable the student to explore particular ideas and realistic case studies of industrial applications; a number of practical examples are included in the text to enhance understanding of points raised, particularly in the areas of mechanics and fluid mechanics; presents the main techniques of perturbation expansion at a level accessible to the undergraduate student.
Author | : Milton D. Van Kyke |
Publisher | : |
Total Pages | : 229 |
Release | : 1964 |
Genre | : Fluid dynamics |
ISBN | : |
Author | : Jens M. Melenk |
Publisher | : Springer |
Total Pages | : 331 |
Release | : 2004-10-19 |
Genre | : Mathematics |
ISBN | : 354045781X |
Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.
Author | : Milton D. Van Dyke |
Publisher | : |
Total Pages | : |
Release | : 1975 |
Genre | : Fluid mechanics |
ISBN | : |
Author | : R.S. Johnson |
Publisher | : Springer Science & Business Media |
Total Pages | : 305 |
Release | : 2005-12-28 |
Genre | : Technology & Engineering |
ISBN | : 0387232176 |
The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems would otherwise have been impossible.