Single Perturbation Problems in Chemical Physics

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Publisher : John Wiley & Sons
ISBN 13 : 047014209X
Total Pages : 390 pages
Book Rating : 4.4/5 (71 download)

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Book Synopsis Single Perturbation Problems in Chemical Physics by : John J. H. Miller

Download or read book Single Perturbation Problems in Chemical Physics written by John J. H. Miller and published by John Wiley & Sons. This book was released on 2009-09-09 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Matching Method for Asymptotic Solutions in Chemical PhysicsProblems by A. M. Il'in, L. A. Kalyakin, and S. I.Maslennikov Singularly Perturbed Problems with Boundary and Interior Layers:Theory and Application by V. F. Butuzov and A. B. Vasilieva Numerical Methods for Singularly Perturbed Boundary Value ProblemsModeling Diffusion Processes by V. L. Kolmogorov and G. I.Shishkin An important addition to the Advances in Chemical Physics series,this volume makes available for the first time in English the workof leading Russian researchers in singular perturbation theory andits application. Since boundary layers were first introduced byPrandtl early in this century, rapid advances have been made in theanalytic and numerical investigation of these phenomena, andnowhere have these advances been more notable than in the Russianschool of singular perturbation theory. The three chapters in thisvolume treat various aspects of singular perturbations and theirnumerical solution, and represent some of the best work done inthis area: * The first chapter, "The Matching Method for Asymptotic Solutionsin Chemical Physics Problems," is concerned with the analysis ofsome singular perturbation problems that arise in chemicalkinetics. In this chapter the matching method is applied to findasymptotic solutions to some dynamical systems of ordinarydifferential equations whose solutions have multiscale timedependence. * The second chapter, "Singularly Perturbed Problems with Boundaryand Interior Layers: Theory and Application," offers acomprehensive overview of the theory and application of asymptoticapproximations for many different kinds of problems in chemicalphysics governed by either ordinary or partial differentialequations with boundary and interior layers. * The third chapter, "Numerical Methods for Singularly PerturbedBoundary Value Problems Modeling Diffusion Processes," discussesthe numerical difficulties that arise in solving the problemsdescribed in the first two chapters, and proposes rigorous criteriafor determining whether or not a numerical method is satisfactoryfor such problems. Methods satisfying these criteria are thenconstructed and applied to obtain numerical solutions to a range ofsample problems. Timely, authoritative, and invaluable to researchers in all areasof chemical physics, Singular Perturbation Problems in ChemicalPhysics is an essential resource.

Advances in Chemical Physics, Single Perturbation Problems in Chemical Physics

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Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (733 download)

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Book Synopsis Advances in Chemical Physics, Single Perturbation Problems in Chemical Physics by : John J. H. Miller

Download or read book Advances in Chemical Physics, Single Perturbation Problems in Chemical Physics written by John J. H. Miller and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Singular Perturbation Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 0387232176
Total Pages : 305 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Singular Perturbation Theory by : R.S. Johnson

Download or read book Singular Perturbation Theory written by R.S. Johnson and published by Springer Science & Business Media. This book was released on 2005-12-28 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems would otherwise have been impossible.

Difference Methods for Singular Perturbation Problems

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Publisher : CRC Press
ISBN 13 : 0203492412
Total Pages : 409 pages
Book Rating : 4.2/5 (34 download)

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Book Synopsis Difference Methods for Singular Perturbation Problems by : Grigory I. Shishkin

Download or read book Difference Methods for Singular Perturbation Problems written by Grigory I. Shishkin and published by CRC Press. This book was released on 2008-09-22 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical methods. The first part of the book e

Numerical Methods for Singularly Perturbed Differential Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 3662032066
Total Pages : 364 pages
Book Rating : 4.6/5 (62 download)

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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.

Numerical Methods for Singularly Perturbed Differential Equations

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Publisher :
ISBN 13 : 9783662032077
Total Pages : 372 pages
Book Rating : 4.0/5 (32 download)

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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 . This book was released on 2014-01-15 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analytical and Numerical Methods for Convection-dominated and Singularly Perturbed Problems

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Publisher : Nova Publishers
ISBN 13 : 9781560728481
Total Pages : 298 pages
Book Rating : 4.7/5 (284 download)

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Book Synopsis Analytical and Numerical Methods for Convection-dominated and Singularly Perturbed Problems by : Lubin Vulkov

Download or read book Analytical and Numerical Methods for Convection-dominated and Singularly Perturbed Problems written by Lubin Vulkov and published by Nova Publishers. This book was released on 2000 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the Proceedings of the Workshop on Analytical and Computational Methods for Convection-Dominated and Singularly Perturbed Problems, which took place in Lozenetz, Bulgaria, 27-31 August 1998. The workshop attracted about 50 participants from 12 countries. The volume includes 13 invited lectures and 19 contributed papers presented at the workshop and thus gives an overview of the latest developments in both the theory and applications of advanced numerical methods to problems having boundary and interior layers. There was an emphasis on experiences from the numerical analysis of such problems and on theoretical developments. The aim of the workshop was to provide an opportunity for scientists from the East and the West, who develop robust methods for singularly perturbed and related problems and also who apply these methods to real-life problems, to discuss recent achievements in this area and to exchange ideas with a view of possible research co-operation.

The Boundary Function Method for Singular Perturbed Problems

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Publisher : SIAM
ISBN 13 : 9781611970784
Total Pages : 234 pages
Book Rating : 4.9/5 (77 download)

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Book Synopsis The Boundary Function Method for Singular Perturbed Problems by : Adelaida B. Vasil'eva

Download or read book The Boundary Function Method for Singular Perturbed Problems written by Adelaida B. Vasil'eva and published by SIAM. This book was released on 1995-01-01 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book published in English devoted solely to the boundary function method, which is one of the asymptotic methods. This method provides an effective and simple way to obtain asymptotic approximations for the solutions of certain ordinary and partial differential equations containing small parameters in front of the highest derivatives. These equations, called singularly perturbed equations, are often used in modeling. In addition to numerous examples, the book includes discussions on singularly perturbed problems from chemical kinetics and heat conduction, semiconductor device modeling, and mathematical biology. The book also contains a variety of original ideas and explicit calculations previously available only in journal literature, as well as many concrete applied problems illustrating the boundary function method algorithms. Quite general asymptotic results described in the book are rigorous in the sense that, along with the asymptotic algorithms, in most cases the theorems on estimation of the remainder terms are presented. A survey of results of Russian mathematicians on the subject is provided; many of these results are not well known in the West. Based on the Russian edition of the textbook by Vasil'eva and Butuzov, this American edition, prepared by Kalachev, differs in many aspects. The text of the book has been revised substantially, some new material has been added to every chapter, and more examples, exercises, and new references on asymptotic methods and their applications have been included.

Introduction to Singular Perturbations

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Publisher :
ISBN 13 : 9780125259507
Total Pages : 206 pages
Book Rating : 4.2/5 (595 download)

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Book Synopsis Introduction to Singular Perturbations by : Robert E. O'Malley

Download or read book Introduction to Singular Perturbations written by Robert E. O'Malley and published by . This book was released on 1974 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Robust Numerical Methods for Singularly Perturbed Differential Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 3540344675
Total Pages : 599 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Robust Numerical Methods for Singularly Perturbed Differential Equations by : Hans-Görg Roos

Download or read book Robust Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2008-09-17 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.

Singular Perturbations in Systems and Control

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Publisher : Springer
ISBN 13 : 370912638X
Total Pages : 337 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Singular Perturbations in Systems and Control by : M.D. Ardema

Download or read book Singular Perturbations in Systems and Control written by M.D. Ardema and published by Springer. This book was released on 2014-05-04 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Solution of Stiff and Singularly Perturbed Problems

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Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659436611
Total Pages : 156 pages
Book Rating : 4.4/5 (366 download)

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Book Synopsis Numerical Solution of Stiff and Singularly Perturbed Problems by : A. M. Nagy

Download or read book Numerical Solution of Stiff and Singularly Perturbed Problems written by A. M. Nagy and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years much attention has been given to the numerical solution of ODEs. Of particular interest has been the solution of singularly perturbed and stiff problems. These types of problems arise in various fields of science and engineering such as fluid mechanics, physics, chemistry, mechanics, chemical reactor theory, convection diffusion processes, optimal control and other branches of applied mathematics. Singular perturbation problems depend on the presence of a small, positive parameter which provides a multi-scale character to the solution. That is the solution varies very rapidly in some parts of the region of integration (layers) and varies slowly in other parts. Stiffness is a property of the differential problem that makes slow and expensive the computation of the numerical solution using classical explicit methods. In this work, we present some numerical methods for solving IVPs and BVBs. Moreover, we give numerical solutions of Volterra integral and integro-differential equations. This book is high recommended to both postgraduate students and researchers in a wide variety of applications.

Introduction to Singular Perturbations. Volume 14. Applied Mathematics and Mechanics

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ISBN 13 :
Total Pages : 215 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Introduction to Singular Perturbations. Volume 14. Applied Mathematics and Mechanics by : Robert E O'Malley (Jr)

Download or read book Introduction to Singular Perturbations. Volume 14. Applied Mathematics and Mechanics written by Robert E O'Malley (Jr) and published by . This book was released on 1974 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces singular perturbation techniques by showing the reader how to obtain asymptotic solutions to several important classes of problems. It concentrates principally on boundary value problems for linear and nonlinear differential equations and includes a detailed treatment of specific examples arising in chemical kinetics and optimal control. Discussion is motivated throughout by simple examples. Particular heuristic ideas that underlie the techniques are developed. The author makes frequent reference to the current literature for applications and generalizations of the topics discussed.

Asymptotics of Elliptic and Parabolic PDEs

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Publisher : Springer
ISBN 13 : 3319768956
Total Pages : 456 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Asymptotics of Elliptic and Parabolic PDEs by : David Holcman

Download or read book Asymptotics of Elliptic and Parabolic PDEs written by David Holcman and published by Springer. This book was released on 2018-05-25 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.

Nonlinear Analysis and Optimization

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Publisher : American Mathematical Soc.
ISBN 13 : 1470417367
Total Pages : 330 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Nonlinear Analysis and Optimization by : Boris S. Mordukhovich

Download or read book Nonlinear Analysis and Optimization written by Boris S. Mordukhovich and published by American Mathematical Soc.. This book was released on 2016-02-26 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the IMU/AMS Special Session on Nonlinear Analysis and Optimization, held from June 16-19, 2014, at the Second Joint International Meeting of the Israel Mathematical Union (IMU) and the American Mathematical Society (AMS), Bar-Ilan and Tel-Aviv Universities, Israel, and the Workshop on Nonlinear Analysis and Optimization, held on June 12, 2014, at the Technion-Israel Institute of Technology. The papers in this volume cover many different topics in Nonlinear Analysis and Optimization, including: Taylor domination property for analytic functions in the complex disk, mappings with upper integral bounds for p -moduli, multiple Fourier transforms and trigonometric series in line with Hardy's variation, finite-parameter feedback control for stabilizing damped nonlinear wave equations, implicit Euler approximation and optimization of one-sided Lipschitz differential inclusions, Bolza variational problems with extended-valued integrands on large intervals, first order singular variational problem with nonconvex cost, gradient and extragradient methods for the elasticity imaging inverse problem, discrete approximations of the entropy functional for probability measures on the plane, optimal irrigation scheduling for wheat production, existence of a fixed point of nonexpansive mappings in uniformly convex Banach spaces, strong convergence properties of m-accretive bounded operators, the Reich-Simons convex analytic inequality, nonlinear input-output equilibrium, differential linear-quadratic Nash games with mixed state-control constraints, and excessive revenue models of competitive markets.

Traveling Wave Solutions of Parabolic Systems

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Publisher : American Mathematical Soc.
ISBN 13 : 9780821897577
Total Pages : 474 pages
Book Rating : 4.8/5 (975 download)

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Book Synopsis Traveling Wave Solutions of Parabolic Systems by : A. I. Volpert

Download or read book Traveling Wave Solutions of Parabolic Systems written by A. I. Volpert and published by American Mathematical Soc.. This book was released on with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of travelling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. With introductory material accessible to non-mathematicians and a nearly complete bibliography of about 500 references, this book is an excellent resource on the subject.

ICIAM '87

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Publisher : SIAM
ISBN 13 : 9780898712247
Total Pages : 412 pages
Book Rating : 4.7/5 (122 download)

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Book Synopsis ICIAM '87 by : James McKenna

Download or read book ICIAM '87 written by James McKenna and published by SIAM. This book was released on 1988-01-01 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: