Asymptotic Methods in the Theory of Linear Differential Equations PDF Download
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Author: Stepan Fedorovich Feshchenko
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 298
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Book Description
Author: Stepan Fedorovich Feshchenko
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 298
Get Book
Book Description
Author: Stepan Fedorovich Feshchenko
Publisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 268
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Book Description
Author: Mikhail V. Fedoryuk
Publisher: Springer Science & Business Media
ISBN: 3642580165
Category : Mathematics
Languages : en
Pages : 370
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Book Description
In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.
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: A. V. Skorokhod
Publisher: American Mathematical Soc.
ISBN: 9780821898253
Category : Mathematics
Languages : en
Pages : 362
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Book Description
Ergodic theorems: General ergodic theorems Densities for transition probabilities and resolvents for Markov solutions of stochastic differential equations Ergodic theorems for one-dimensional stochastic equations Ergodic theorems for solutions of stochastic equations in $R^d$ Asymptotic behavior of systems of stochastic equations containing a small parameter: Equations with a small right-hand side Processes with rapid switching Averaging over variables for systems of stochastic differential equations Stability. Linear systems: Stability of sample paths of homogeneous Markov processes Linear equations in $R^d$ and the stochastic semigroups connected with them. Stability Stability of solutions of stochastic differential equations Linear stochastic equations in Hilbert space. Stochastic semigroups. Stability: Linear equations with bounded coefficients Strong stochastic semigroups with second moments Stability Bibliography
Author: David Y. Gao
Publisher: CRC Press
ISBN: 1420011731
Category : Mathematics
Languages : en
Pages : 270
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Book Description
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
Author: Nikolaĭ Nikolaevich Bogoli︠u︡bov
Publisher: CRC Press
ISBN: 9780677200507
Category : Science
Languages : en
Pages : 556
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Author: Sigrun Bodine
Publisher: Springer
ISBN: 331918248X
Category : Mathematics
Languages : en
Pages : 402
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Book Description
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to non-experts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites.
Author: A. V. Skorokhod
Publisher: American Mathematical Soc.
ISBN: 9780821846865
Category : Mathematics
Languages : en
Pages : 339
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Book Description
Written by one of the foremost Soviet experts in the field, this book is intended for specialists in the theory of random processes and its applications. The author's 1982 monograph on stochastic differential equations, written with Iosif Ilich Gikhman, did not include a number of topics important to applications. The present work begins to fill this gap by investigating the asymptotic behavior of stochastic differential equations. The main topics are ergodic theory for Markov processes and for solutions of stochastic differential equations, stochastic differential equations containing a small parameter, and stability theory for solutions of systems of stochastic differential equations.
Author: Anatoliĭ Vladimirovich Skorokhod
Publisher: Amer Mathematical Society
ISBN: 9780821845318
Category : Mathematics
Languages : en
Pages : 339
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Book Description
