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Numerical Integration Of Asymptotic Solutions Of Ordinary Differential Equations
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Author :National Aeronautics and Space Administration (NASA) Publisher :Createspace Independent Publishing Platform ISBN 13 :9781722423148 Total Pages :44 pages Book Rating :4.4/5 (231 download)
Book Synopsis Numerical Integration of Asymptotic Solutions of Ordinary Differential Equations by : National Aeronautics and Space Administration (NASA)
Download or read book Numerical Integration of Asymptotic Solutions of Ordinary Differential Equations written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-11 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration. Thurston, Gaylen A. Langley Research Center RTOP 505-63-01-08...
Book Synopsis Numerical Integration of Asymptotic Solutions of Ordinary Differential Equations by :
Download or read book Numerical Integration of Asymptotic Solutions of Ordinary Differential Equations written by and published by . This book was released on 1989 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Integration of Asymptotic Solutions of Ordinary Differential Equations by : G. A. Thurston
Download or read book Numerical Integration of Asymptotic Solutions of Ordinary Differential Equations written by G. A. Thurston and published by . This book was released on 1989 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Integration of Differential and Difference Equations by : Sigrun Bodine
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 411 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.
Book Synopsis Asymptotic Analysis of Differential Equations by : R. B. White
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.
Book Synopsis Asymptotic Expansions for Ordinary Differential Equations by : Wolfgang Wasow
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.
Book Synopsis Asymptotic Analysis by : Mikhail V. Fedoryuk
Download or read book Asymptotic Analysis written by Mikhail V. Fedoryuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Methods for Singularly Perturbed Differential Equations by : Hans-Görg Roos
Download or read book Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.
Book Synopsis Asymptotic Solutions of Differential Equations and Their Applications by : Calvin Hayden Wilcox
Download or read book Asymptotic Solutions of Differential Equations and Their Applications written by Calvin Hayden Wilcox and published by . This book was released on 1964 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Analysis and the Numerical Solution of Partial Differential Equations by : Hans G. Kaper
Download or read book Asymptotic Analysis and the Numerical Solution of Partial Differential Equations written by Hans G. Kaper and published by CRC Press. This book was released on 1991-02-25 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
Book Synopsis Asymptotic Behavior of Solutions of Differential-Difference Equations by : Richard Bellman
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:
Book Synopsis Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters by : H.G. Kaper
Download or read book Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters written by H.G. Kaper and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NATO Advanced Research Workshop on "Asymptotic-induced Numerical Methods for Partial Differ ential Equations, Critical Parameters, and Domain Decomposition," held at Beaune (France), May 25-28, 1992. The purpose of the workshop was to stimulate the integration of asymp totic analysis, domain decomposition methods, and symbolic manipulation tools for the numerical solution of partial differential equations (PDEs) with critical parameters. A workshop on the same topic was held at Argonne Na tional Laboratory in February 1990. (The proceedings were published under the title Asymptotic Analysis and the Numerical Solu.tion of Partial Differ ential Equations, Hans G. Kaper and Marc Garbey, eds., Lecture Notes in Pure and Applied Mathematics. Vol. 130, ·Marcel Dekker, Inc., New York, 1991.) In a sense, the present proceedings represent a progress report on the topic area. Comparing the two sets of proceedings, we see an increase in the quantity as well as the quality of the contributions. 110re research is being done in the topic area, and the interest covers serious, nontrivial problems. We are pleased with this outcome and expect to see even more advances in the next few years as the field progresses.
Book Synopsis Numerical Solution of Ordinary Differential Equations by : Kendall Atkinson
Download or read book Numerical Solution of Ordinary Differential Equations written by Kendall Atkinson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.
Book Synopsis Asymptotic Behavior of Monodromy by : Carlos Simpson
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.
Book Synopsis Surveys in Applied Mathematics by : Joseph B. Keller
Download or read book Surveys in Applied Mathematics written by Joseph B. Keller and published by Springer. This book was released on 2013-12-21 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations play a central role in many branches of science and engineering. Therefore it is important to solve problems involving them. One aspect of solving a partial differential equation problem is to show that it is well-posed, i. e. , that it has one and only one solution, and that the solution depends continuously on the data of the problem. Another aspect is to obtain detailed quantitative information about the solution. The traditional method for doing this was to find a representation of the solution as a series or integral of known special functions, and then to evaluate the series or integral by numerical or by asymptotic methods. The shortcoming of this method is that there are relatively few problems for which such representations can be found. Consequently, the traditional method has been replaced by methods for direct solution of problems either numerically or asymptotically. This article is devoted to a particular method, called the "ray method," for the asymptotic solution of problems for linear partial differential equations governing wave propagation. These equations involve a parameter, such as the wavelength. . \, which is small compared to all other lengths in the problem. The ray method is used to construct an asymptotic expansion of the solution which is valid near . . \ = 0, or equivalently for k = 21r I A near infinity.
Book Synopsis Introduction to Ordinary Differential Equations with Mathematica by : Alfred Gray
Download or read book Introduction to Ordinary Differential Equations with Mathematica written by Alfred Gray and published by Springer. This book was released on 1997-06-20 with total page 920 pages. Available in PDF, EPUB and Kindle. Book excerpt: These materials - developed and thoroughly class tested over many years by the authors -are for use in courses at the sophomore/junior level. A prerequisite is the calculus of one variable, although calculus of several variables, and linear algebra are recommended. The text covers the standard topics in first and second order equations, power series solutions, first order systems, Laplace transforms, numerical methods and stability of non-linear systems. Liberal use is made of programs in Mathematica, both for symbolic computations and graphical displays. The programs are described in separate sections, as well as in the accompanying Mathematica notebooks. However, the book has been designed so that it can be read with or without Mathematica and no previous knowledge of Mathematica is required. The CD-ROM contains the Mathematica solution of worked examples, a selection of various Mathematica notebooks, Mathematica movies and sample labs for students. Mathematica programs and additional problem/example files will be available online through the TELOS Web site and the authors dedicated web site.
Book Synopsis Asymptotic Solutions of Differential Equations with Transition Points by : Arthur Erdélyi
Download or read book Asymptotic Solutions of Differential Equations with Transition Points written by Arthur Erdélyi and published by . This book was released on 1956 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:
