The Asymptotic Solution of Differential Equations with a Turning Point and Singularities PDF Download

Author: R. C. Thorne
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 22

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Author: Wolfgang Wasow
Publisher: Courier Dover Publications
ISBN: 0486824586
Category : Mathematics
Languages : en
Pages : 385

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This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.

Author: Frank W. J. Olver
Publisher: World Scientific
ISBN: 9789810249946
Category : Asymptotic expansions
Languages : en
Pages : 548

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Author: Arthur Erdélyi
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 182

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Author: P. A. Martin
Publisher: Cambridge University Press
ISBN: 9780521414142
Category : Mathematics
Languages : en
Pages : 262

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This volume contains papers by distinguished researchers in fluid mechanics and asymptotics. The papers collected here outline the development of these topics.

Author: Wolfgang Wasow
Publisher: Springer Science & Business Media
ISBN: 1461210909
Category : Mathematics
Languages : en
Pages : 255

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My book "Asymptotic Expansions for Ordinary Differential Equations" published in 1965 is out of print. In the almost 20 years since then, the subject has grown so much in breadth and in depth that an account of the present state of knowledge of all the topics discussed there could not be fitted into one volume without resorting to an excessively terse style of writing. Instead of undertaking such a task, I have concentrated, in this exposi tion, on the aspects of the asymptotic theory with which I have been particularly concerned during those 20 years, which is the nature and structure of turning points. As in Chapter VIII of my previous book, only linear analytic differential equations are considered, but the inclusion of important new ideas and results, as well as the development of the neces sary background material have made this an exposition of book length. The formal theory of linear analytic differential equations without a parameter near singularities with respect to the independent variable has, in recent years, been greatly deepened by bringing to it methods of modern algebra and topology. It is very probable that many of these ideas could also be applied to the problems concerning singularities with respect to a parameter, and I hope that this will be done in the near future. It is less likely, however, that the analytic, as opposed to the formal, aspects of turning point theory will greatly benefit from such an algebraization.

Author: F. W. J. Olver
Publisher: Academic Press
ISBN: 148326744X
Category : Mathematics
Languages : en
Pages : 589

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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.

Author: Richard E. Meyer
Publisher: Academic Press
ISBN: 1483264572
Category : Mathematics
Languages : en
Pages : 418

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Mathematics Research Center Symposia and Advanced Seminar Series: Singular Perturbations and Asymptotics covers the lectures presented at an Advanced Seminar on Singular Perturbation and Asymptotics, held in Madison, Wisconsin on May 28-30, 1980 under the auspices of the Mathematics Research Center of the University of Wisconsin—Madison. The book focuses on the processes, methodologies, reactions, and principles involved in singular perturbations and asymptotics, including boundary value problems, equations, perturbations, water waves, and gas dynamics. The selection first elaborates on basic concepts in the analysis of singular perturbations, limit process expansions and approximate equations, and results on singularly perturbed boundary value problems. Discussions focus on quasi-linear and nonlinear problems, semilinear systems, water waves, expansion in gas dynamics, asymptotic matching principles, and classical perturbation analysis. The text then takes a look at multiple solutions of singularly perturbed systems in the conditionally stable case and singular perturbations, stochastic differential equations, and applications. The book ponders on connection problems in the parameterless case; general connection-formula problem for linear differential equations of the second order; and turning-point problems for ordinary differential equations of hydrodynamic type. Topics include the comparison equation method, boundary layer flows, compound matrix method, asymptotic solution of the connection-formula problem, and higher order equations. The selection is a valuable source of information for researchers interested in singular perturbations and asymptotics.

Author: Alexander G. Ramm
Publisher: Springer Science & Business Media
ISBN: 1489915524
Category : Mathematics
Languages : en
Pages : 207

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Proceedings of Sessions from the First Congress of the International Society for Analysis, Applications and Computing held in Newark, Delaware, June, 2-, 1997

Author:
Publisher:
ISBN:
Category : Military research
Languages : en
Pages : 834

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