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Asymptotic Methods In Equations Of Mathematical Physics
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Book Synopsis Asymptotic Methods in Equations of Mathematical Physics by : B Vainberg
Download or read book Asymptotic Methods in Equations of Mathematical Physics written by B Vainberg and published by CRC Press. This book was released on 1989-02-25 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Typed English translation of a monograph first published (in Russian) in 1982. Provides graduate students and researchers with usefully detailed discussion of most of the asymptotic methods standard these days to the work of mathematical physicists. The author prefers not to dwell in the heights of abstraction; he has written a broadly intelligble book, which is informed at every point by his secure command of major physical applications. An expensive but valuable contribution to the literature of an important but too-little-written- about field. Twelve chapters, references. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Introduction to Asymptotic Methods by : David Y. Gao
Download or read book Introduction to Asymptotic Methods written by David Y. Gao and published by CRC Press. This book was released on 2006-05-03 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m
Book Synopsis Partial Differential Equations V by : M.V. Fedoryuk
Download or read book Partial Differential Equations V written by M.V. Fedoryuk and published by Springer. This book was released on 2011-09-27 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.
Book Synopsis Differential Equations and Asymptotic Theory in Mathematical Physics by : Chen Hua
Download or read book Differential Equations and Asymptotic Theory in Mathematical Physics written by Chen Hua and published by World Scientific. This book was released on 2004-10-18 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Lectures on Orthogonal Polynomials (M E H Ismail)Gevrey Asymptotics and Applications to Holomorphic Ordinary Differential Equations (J-P Ramis)Spikes for Singularly Perturbed Reaction-Diffusion Systems and Carrier's Problem (M J Ward)Five Lectures on Asymptotic Theory (R S C Wong)A Perturbation Model for the Growth of Type III-V Compound Crystals (C S Bohun et al.)Asymptotic Behaviour of the Trace for Schrödinger Operator on Irregular Domains (H Chen & C Yu)Limitations and Modifications of Black-Scholes Model (L S Jiang & X M Ren)Exact Boundary Controllability of Unsteady Flows in a Network of Open Canals (T T Li)Hierarchy of Partial Differential Equations and Fundamental Solutions Associated with Summable Formal Solutions of a Partial Differential Equations of non Kowalevski Type (M Miyake & K Ichinobe)On the Singularities of Solutions of Nonlinear Partial Differential Equations in the Complex Domain, II (H Tahara)Identifying Corrosion Boundary by Perturbation Method (Y J Tan & X X Chen)Existence and Stability of Lamellar and Wriggled Lamellar Solutions in the Diblock Copolymer Problem (J C Wei) Readership: Graduate students, researchers, academics and lecturers in mathematical physics. Keywords:Asymptotic Theory;Special Functions;Orthogonal Polynomials;Singular Perturbations;Reaction Diffusion Equations;Gevrey Asymptotics;Stationary Phase Approximation;WKB Method
Book Synopsis Partial Differential Equations V by : M.V. Fedoryuk
Download or read book Partial Differential Equations V written by M.V. Fedoryuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.
Book Synopsis Asymptotic Methods for Wave and Quantum Problems by : M. V. Karasev
Download or read book Asymptotic Methods for Wave and Quantum Problems written by M. V. Karasev and published by American Mathematical Soc.. This book was released on 2003 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper ``Quantization and Intrinsic Dynamics'' a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approximation method. It also explains a hidden dynamic geometry that arises when using these methods. Three other papers discuss applications of asymptotic methods to the construction of wave-type solutions of nonlinear PDE's, to the theory of semiclassical approximation (in particular, the Whitham method) for nonlinear second-order ordinary differential equations, and to the study of the Schrodinger type equations whose potential wells are sufficiently shallow that the discrete spectrum contains precisely one point. All the papers contain detailed references and are oriented not only to specialists in asymptotic methods, but also to a wider audience of researchers and graduate students working in partial differential equations and mathematical physics.
Book Synopsis Advanced Mathematical Methods for Scientists and Engineers I by : Carl M. Bender
Download or read book Advanced Mathematical Methods for Scientists and Engineers I written by Carl M. Bender and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains by : Dmitrii Korikov
Download or read book Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains written by Dmitrii Korikov and published by Springer Nature. This book was released on 2021-04-01 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.
Book Synopsis Asymptotic Analysis Of Differential Equations (Revised Edition) by : White Roscoe B
Download or read book Asymptotic Analysis Of Differential Equations (Revised Edition) written by White Roscoe B and published by World Scientific. This book was released on 2010-08-16 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.
Book Synopsis Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications by : Johan Grasman
Download or read book Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications written by Johan Grasman and published by Springer Science & Business Media. This book was released on 1999-03-08 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.
Book Synopsis Asymptotic Methods for Integrals by : Nico M. Temme
Download or read book Asymptotic Methods for Integrals written by Nico M. Temme and published by World Scientific Publishing Company. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals. The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.
Book Synopsis Asymptotic Methods for Engineers by : Igor V. Andrianov
Download or read book Asymptotic Methods for Engineers written by Igor V. Andrianov and published by CRC Press. This book was released on 2024-05-20 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Methods for Engineers is based on the authors’ many years of practical experience in the application of asymptotic methods to solve engineering problems. This book is devoted to modern asymptotic methods (AM), which is widely used in engineering, applied sciences, physics, and applied mathematics. Avoiding complex formal calculations and justifications, the book’s main goal is to describe the main ideas and algorithms. Moreover, not only is there a presentation of the main AM, but there is also a focus on demonstrating their unity and inseparable connection with the methods of summation and asymptotic interpolation. The book will be useful for students and researchers from applied mathematics and physics and of interest to doctoral and graduate students, university and industry professors from various branches of engineering (mechanical, civil, electro-mechanical, etc.).
Book Synopsis Semi-Classical Approximation in Quantum Mechanics by : Victor P. Maslov
Download or read book Semi-Classical Approximation in Quantum Mechanics written by Victor P. Maslov and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is concerned with a detailed description of the canonical operator method - one of the asymptotic methods of linear mathematical physics. The book is, in fact, an extension and continuation of the authors' works [59], [60], [65]. The basic ideas are summarized in the Introduction. The book consists of two parts. In the first, the theory of the canonical operator is develop ed, whereas, in the second, many applications of the canonical operator method to concrete problems of mathematical physics are presented. The authors are pleased to express their deep gratitude to S. M. Tsidilin for his valuable comments. THE AUTHORS IX INTRODUCTION 1. Various problems of mathematical and theoretical physics involve partial differential equations with a small parameter at the highest derivative terms. For constructing approximate solutions of these equations, asymptotic methods have long been used. In recent decades there has been a renaissance period of the asymptotic methods of linear mathematical physics. The range of their applicability has expanded: the asymptotic methods have been not only continuously used in traditional branches of mathematical physics but also have had an essential impact on the development of the general theory of partial differential equations. It appeared recently that there is a unified approach to a number of problems which, at first sight, looked rather unrelated.
Book Synopsis Theory And Applications In Mathematical Physics: In Honor Of B Tirozzi's 70th Birthday by : Montani Giovanni
Download or read book Theory And Applications In Mathematical Physics: In Honor Of B Tirozzi's 70th Birthday written by Montani Giovanni and published by World Scientific. This book was released on 2015-10-13 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to make a connection among advanced mathematical tools and application to real problems. There are many different mathematical structures analyzed in the book and all of them are in important applications, like statistics and biology, neural networks and financial markets, asymptotic methods for partial differential equations and the problem of tsunami propagation. Plasma physics has been given a new approach, using focal points in analogy to the theory of tsunami waves.
Book Synopsis Asymptotic Theory of Separated Flows by : Vladimir V. Sychev
Download or read book Asymptotic Theory of Separated Flows written by Vladimir V. Sychev and published by Cambridge University Press. This book was released on 1998-08-28 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary-layer separation from a rigid body surface is one of the fundamental problems of classical and modern fluid dynamics. The major successes achieved since the late 1960s in the development of the theory of separated flows at high Reynolds numbers are in many ways associated with the use of asymptotic methods. The most fruitful of these has proved to be the method of matched asymptotic expansions, which has been widely used in mechanics and mathematical physics. There have been many papers devoted to different problems in the asymptotic theory of separated flows and we can confidently speak of the appearance of a very productive direction in the development of theoretical hydrodynamics. This book will present this theory in a systematic account. The book will serve as a useful introduction to the theory, and will draw attention to the possibilities that application of the asymptotic approach provides.
Book Synopsis Asymptotology by : Igor V. Andrianov
Download or read book Asymptotology written by Igor V. Andrianov and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods belong to the, perhaps, most romantic area of modern mathematics. They are widely known and have been used in me chanics, physics and other exact sciences for many, many decades. But more than this, asymptotic ideas are found in all branches of human knowledge, indeed in all areas of life. In this broader context they have not and perhaps cannot be fully formalized. However, they are mar velous, they leave room for fantasy, guesses and intuition; they bring us very near to the border of the realm of art. Many books have been written and published about asymptotic meth ods. Most of them presume a mathematically sophisticated reader. The authors here attempt to describe asymptotic methods on a more accessi ble level, hoping to address a wider range of readers. They have avoided the extreme of banishing formulae entirely, as done in some popular science books that attempt to describe mathematical methods with no mathematics. This is impossible (and not wise). Rather, the authors have tried to keep the mathematics at a moderate level. At the same time, using simple examples, they think they have been able to illustrate all the key ideas of asymptotic methods and approaches, to depict in de tail the results of their application to various branches of knowledg- from astronomy, mechanics, and physics to biology, psychology and art. The book is supplemented by several appendices, one of which con tains the profound ideas of R. G.
Book Synopsis Asymptotic Expansion of a Partition Function Related to the Sinh-model by : Gaëtan Borot
Download or read book Asymptotic Expansion of a Partition Function Related to the Sinh-model written by Gaëtan Borot and published by Springer. This book was released on 2016-12-08 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.
