Asymptotics Of High Order Differential Equations
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Asymptotics Of High Order Differential Equations
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Author : R. B. Paris
language : en
Publisher: Longman Scientific and Technical
Release Date : 1986
Asymptotics Of High Order Differential Equations written by R. B. Paris and has been published by Longman Scientific and Technical this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Asymptotics Of High Order Differential Equations
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Author : R. B. Paris
language : en
Publisher: Longman
Release Date : 1986
Asymptotics Of High Order Differential Equations written by R. B. Paris and has been published by Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
Asymptotics Of Linear Differential Equations
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Author : M.H. Lantsman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Asymptotics Of Linear Differential Equations written by M.H. Lantsman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural sci ence bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymp totic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects.
Higher Order Time Asymptotics Of Fast Diffusion In Euclidean Space A Dynamical Systems Approach
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Author : Jochen Denzler
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-02-06
Higher Order Time Asymptotics Of Fast Diffusion In Euclidean Space A Dynamical Systems Approach written by Jochen Denzler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-06 with Mathematics categories.
This paper quantifies the speed of convergence and higher-order asymptotics of fast diffusion dynamics on Rn to the Barenblatt (self similar) solution. Degeneracies in the parabolicity of this equation are cured by re-expressing the dynamics on a manifold with a cylindrical end, called the cigar. The nonlinear evolution becomes differentiable in Hölder spaces on the cigar. The linearization of the dynamics is given by the Laplace-Beltrami operator plus a transport term (which can be suppressed by introducing appropriate weights into the function space norm), plus a finite-depth potential well with a universal profile. In the limiting case of the (linear) heat equation, the depth diverges, the number of eigenstates increases without bound, and the continuous spectrum recedes to infinity. The authors provide a detailed study of the linear and nonlinear problems in Hölder spaces on the cigar, including a sharp boundedness estimate for the semigroup, and use this as a tool to obtain sharp convergence results toward the Barenblatt solution, and higher order asymptotics. In finer convergence results (after modding out symmetries of the problem), a subtle interplay between convergence rates and tail behavior is revealed. The difficulties involved in choosing the right functional spaces in which to carry out the analysis can be interpreted as genuine features of the equation rather than mere annoying technicalities.
Asymptotic Treatment Of Differential Equations
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Author : A. Georgescu
language : en
Publisher: CRC Press
Release Date : 1995-05-15
Asymptotic Treatment Of Differential Equations written by A. Georgescu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-05-15 with Mathematics categories.
The main definitions and results of asymptotic analysis and the theory of regular and singular perturbations are summarized in this book. They are applied to the asymptotic study of several mathematical models from mechanics, fluid dynamics, statistical mechanics, meteorology and elasticity. Due to the generality of presentation this applications-oriented book is suitable for the solving of differential equations from any other field of interest.
Asymptotics And Mellin Barnes Integrals
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Author : R. B. Paris
language : en
Publisher: Cambridge University Press
Release Date : 2001-09-24
Asymptotics And Mellin Barnes Integrals written by R. B. Paris and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-09-24 with Mathematics categories.
Asymptotics and Mellin-Barnes Integrals, first published in 2001, provides an account of the use and properties of a type of complex integral representation that arises frequently in the study of special functions typically of interest in classical analysis and mathematical physics. After developing the properties of these integrals, their use in determining the asymptotic behaviour of special functions is detailed. Although such integrals have a long history, the book's account includes recent research results in analytic number theory and hyperasymptotics. The book also fills a gap in the literature on asymptotic analysis and special functions by providing a thorough account of the use of Mellin-Barnes integrals that is otherwise not available in other standard references on asymptotics.
Higher Order Asymptotics
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Author : J. K. Ghosh
language : en
Publisher: IMS
Release Date : 1994
Higher Order Asymptotics written by J. K. Ghosh and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Asymptotics And Special Functions
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Author : F. W. J. Olver
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Asymptotics And Special Functions written by F. W. J. Olver and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.
Wavefronts And Rays As Characteristics And Asymptotics Third Edition
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Author : Andrej Bona
language : en
Publisher: World Scientific
Release Date : 2020-09-24
Wavefronts And Rays As Characteristics And Asymptotics Third Edition written by Andrej Bona and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-24 with Science categories.
Characteristics and asymptotics of partial differential equations play an important role in mathematical physics since they lead to insightful solutions of complex problems that might not be solvable otherwise. They constitute, however, a difficult subject, and the purpose of this book, with its additions and refinements that led to its third edition, is to present this subject in an accessible manner, without decreasing the rigor. As any method, characteristics and asymptotics have their limitations. This important issue is addressed in the last chapter, where we discuss caustics, which must be understood in applications of the method, and which constitute a fertile ground for further mathematical research.The book is both a research reference and a textbook. Its careful and explanatory style, which includes numerous exercises with detailed solutions, makes it an excellent textbook for senior undergraduate and graduate courses, as well as for independent studies. Six appendices are provided, which form a self-contained course on applied mathematics and can be used as a textbook on its own.
Approximate Analytical Methods For Solving Ordinary Differential Equations
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Author : T.S.L Radhika
language : en
Publisher: CRC Press
Release Date : 2014-11-21
Approximate Analytical Methods For Solving Ordinary Differential Equations written by T.S.L Radhika and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-21 with Mathematics categories.
Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solut