Download or read book Asymptotic Integration of Differential and Difference Equations written by Sigrun Bodine and published by Springer. This book was released on 2015-05-26 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Asymptotic Behavior of Solutions of Differential Difference Equations written by Richard Bellman and published by American Mathematical Soc.. This book was released on 1959 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Analysis of Differential Equations written by R. B. White and published by World Scientific. This book was released on 2010 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Download or read book Asymptotic Behavior of Solutions of Differential difference Equations written by and published by . This book was released on 1958 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the problem was considered of determining the asymptotic behavior of solutions of linear differentialdifference equations whose coefficients possess asymptotic series. Although the problem is considerably more complicated than the corresponding problem for ordinary differential equations, by means of a sequence of transformations the problem was reduced to a form where the standard techniques of ordinary differential equation theory could be employed. The differential-difference equation was transformed into an integral equation which was trans formed into an integro-differential equation. At this point the Liouville transformation plays a vital role. Although the guiding ideas were simple, the analysis became formidable. For this reason, only some of the more immediate aspects of the problem were considered.
Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Wasow and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Asymptotic Integration And Stability For Ordinary Functional And Discrete Differential Equations Of Fractional Order written by Dumitru Baleanu and published by World Scientific. This book was released on 2015-01-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents several important and recent contributions to the emerging field of fractional differential equations in a self-contained manner. It deals with new results on existence, uniqueness and multiplicity, smoothness, asymptotic development, and stability of solutions. The new topics in the field of fractional calculus include also the Mittag-Leffler and Razumikhin stability, stability of a class of discrete fractional non-autonomous systems, asymptotic integration with a priori given coefficients, intervals of disconjugacy (non-oscillation), existence of Lp solutions for various linear, and nonlinear fractional differential equations.
Download or read book Asymptotic Integration and Stability written by Dumitru Baleanu and published by Series on Complexity, Nonlinearity, and Chaos. This book was released on 2015 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents several important and recent contributions to the emerging field of fractional differential equations in a self-contained manner. It deals with new results on existence, uniqueness and multiplicity, smoothness, asymptotic development, and stability of solutions. The new topics in the field of fractional calculus include also the Mittag-Leffler and Razumikhin stability, stability of a class of discrete fractional non-autonomous systems, asymptotic integration with a priori given coefficients, intervals of disconjugacy (non-oscillation), existence of Lp solutions for various linear, and nonlinear fractional differential equations.
Download or read book Introduction to Asymptotics and Special Functions written by F. W. J. Olver and published by Academic Press. This book was released on 2014-05-10 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Asymptotics and Special Functions is a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable are discussed, along with contour integrals and differential equations with regular and irregular singularities. The Liouville-Green approximation is also considered. Comprised of seven chapters, this volume begins with an overview of the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on integrals of a real variable. Contour integrals are then examined, paying particular attention to Laplace integrals with a complex parameter and Bessel functions of large argument and order. Subsequent chapters focus on differential equations having regular and irregular singularities, with emphasis on Legendre functions as well as Bessel and confluent hypergeometric functions. A chapter devoted to the Liouville-Green approximation tackles asymptotic properties with respect to parameters and to the independent variable, eigenvalue problems, and theorems on singular integral equations. This monograph is intended for students needing only an introductory course to asymptotics and special functions.
Download or read book Asymptotics of High Order Differential Equations written by R. B. Paris and published by Longman. This book was released on 1986 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Treatment of Differential Equations written by A. Georgescu and published by CRC Press. This book was released on 1995-05-15 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Asymptotic Integration Algorithms for Nonhomogeneous Nonlinear First Order Ordinary Differential Equations written by and published by . This book was released on 1991 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book International Conference on Differential Equations written by H.A. Antosiewicz and published by Academic Press. This book was released on 2014-05-10 with total page 857 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Conference on Differential Equations contains the proceedings of an International Conference on Differential Equations held at the University of Southern California, on September 3-7, 1974. The papers review advances in the qualitative-analytic theory of differential equations and highlight three broad areas: analytic theory (singular perturbations), qualitative theory (boundary value problems), and mathematical control theory (variational methods). Comprised of 82 chapters, this book begins with a discussion on continuous extensions, their construction, and their application in the theory of differential equations. The reader is then introduced to an approach to boundary control of partial differential equations based on the theory of semigroups of operators; lower closure and existence theorems in optimal control; and a nonlinear oscillation theorem. Subsequent chapters focus on matrices of rational functions; asymptotic integration of linear differential systems; solutions near bifurcated steady states; and geometric views in existence theory. This monograph will be of interest to students and instructors of mathematics.
Download or read book Asymptotics and Special Functions written by F. W. J. Olver and published by Academic Press. This book was released on 2014-05-10 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Asymptotic Behavior of Monodromy written by Carlos Simpson and published by Springer. This book was released on 2006-11-14 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give nonzero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go to infinity. A particular classof families of equations is considered, where the answer exhibits a new kind of behavior not seen in most work known until now. The techniques include Laplace transform and the method of stationary phase, and a combinatorial technique for estimating the contributions of terms in an infinite series expansion for the solution. Addressed primarily to researchers inalgebraic geometry, ordinary differential equations and complex analysis, the book will also be of interest to applied mathematicians working on asymptotics of singular perturbations and numerical solution of ODE's.
Download or read book Impulsive Differential Equations Asymptotic Properties Of The Solutions written by Drumi D Bainov and published by World Scientific. This book was released on 1995-03-29 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.
Download or read book Asymptotic Analysis written by Mikhail Vasilʹevich Fedori︠u︡k and published by Springer. This book was released on 1993 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Analysis of Differential Equations Revised Edition written by Roscoe B. White and published by . This book was released on 2010 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt:
