Asymptotic Expansions of Solutions of Differential Linear Equations of the Second Order in a Complex Domain PDF Download
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Author: Mikhail Vasilʹevich Fedori︠u︡k
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 46
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Book Description
Second order linear ordinary differential equations whose highest derivative is multiplied by a small parameter are solved by asymptotic series valid in unbounded domains and the connecting formulas across the Stokes lines are determined. (Author).
Author: Mikhail Vasilʹevich Fedori︠u︡k
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 46
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Book Description
Second order linear ordinary differential equations whose highest derivative is multiplied by a small parameter are solved by asymptotic series valid in unbounded domains and the connecting formulas across the Stokes lines are determined. (Author).
Author:
Publisher: Elsevier
ISBN: 0080871291
Category : Mathematics
Languages : en
Pages : 307
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Book Description
Global Theory of a Second Order Linear Ordinary Differential Equation with a Polynomial Coefficient
Author: Wolfgang Wasow
Publisher: Courier Dover Publications
ISBN: 0486824586
Category : Mathematics
Languages : en
Pages : 385
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Book Description
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: Augustin Fruchard
Publisher: Springer
ISBN: 3642340350
Category : Mathematics
Languages : en
Pages : 169
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Book Description
The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance problem is solved.
Author: R. B. White
Publisher: World Scientific
ISBN: 1848166087
Category : Mathematics
Languages : en
Pages : 430
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Book Description
"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
Author: Johannes Gualtherus van der Corput
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 356
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Book Description
Author: Mikhail Vasilʹevich Fedori︠u︡k
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 384
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Book Description
Author: R. C. Thorne
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 140
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Book Description
Author: F. W. J. Olver
Publisher: Academic Press
ISBN: 148326744X
Category : Mathematics
Languages : en
Pages : 589
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Book Description
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: Frank Olver
Publisher: CRC Press
ISBN: 1439864543
Category : Mathematics
Languages : en
Pages : 591
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Book Description
A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool.
