Author: Publisher:
ISBN:
Category :
Languages : en
Pages : 24
Book Description
Solution of Second-order Linear System by Matched Asymptotic Expansions
Author: Solution of Second-Order Linear System by Matched Asymptotic Expansions
Author: National Aeronautics and Space Administration (NASA)Publisher: Createspace Independent Publishing Platform
ISBN: 9781723416996
Category :
Languages : en
Pages : 24
Book Description
Matched asymptotic expansions (MAE) are used to obtain a first order approximation to the solution of a singularly perturbed second order system. A special case is considered in which the uniform asymptotic solution obtained by MAE is shown to converge to the exact solution. Ways in which the method can be used to sole higher-order linear systems, including those which are not singularly perturbed, are also discussed. Ardema, M. D. Ames Research Center NASA-TM-84246, A-8938, NAS 1.15:84246 RTOP 307-01-00
Matched Asymptotic Expansions and Singular Perturbations
Author: Wiktor EckhausPublisher: Elsevier Science & Technology
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 168
Book Description
Matched Asymptotic Expansions
Author: P.A. LagerstromPublisher: Springer Science & Business Media
ISBN: 1475719906
Category : Mathematics
Languages : en
Pages : 263
Book Description
Content and Aims of this Book Earlier drafts of the manuscript of this book (James A. Boa was then coau thor) contained discussions of many methods and examples of singular perturba tion problems. The ambitious plans of covering a large number of topics were later abandoned in favor of the present goal: a thorough discussion of selected ideas and techniques used in the method of matched asymptotic expansions. Thus many problems and methods are not covered here: the method of av eraging and the related method of multiple scales are mentioned mainly to give reasons why they are not discussed further. Examples which required too sophis ticated and involved calculations, or advanced knowledge of a special field, are not treated; for instance, to the author's regret some very interesting applications to fluid mechanics had to be omitted for this reason. Artificial mathematical examples introduced to show some exotic or unexpected behavior are omitted, except when they are analytically simple and are needed to illustrate mathematical phenomena important for realistic problems. Problems of numerical analysis are not discussed.
Solution of Linear Systems by a Singular Perturbation Technique
Author: Asymptotic Expansions: The asymptotic behaviour of the real solutions of certain second order differential equations
Author: Johannes Gualtherus van der CorputPublisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 356
Book Description
Asymptotic Expansions of Solutions of Differential Linear Equations of the Second Order in a Complex Domain
Author: Mikhail Vasilʹevich Fedori︠u︡kPublisher:
ISBN:
Category : Asymptotic expansions
Languages : en
Pages : 46
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).
The asymptotic solution of linear second order differential equations in a domain containing a turning point and regular singularity
Author: R. C. ThornePublisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 140
Book Description
Singular Perturbations and Asymptotics
Author: Richard E. MeyerPublisher: Academic Press
ISBN: 1483264572
Category : Mathematics
Languages : en
Pages : 418
Book Description
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.
Matching of Asymptotic Expansions of Solutions of Boundary Value Problems
Author: A. M. Ilʹin A. M. Il'inPublisher: American Mathematical Soc.
ISBN: 9780821897348
Category : Asymptotic expansions
Languages : en
Pages : 754
Book Description
