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Book Group Analysis of Differential Equations

Download or read book Group Analysis of Differential Equations written by L. V. Ovsiannikov and published by Academic Press. This book was released on 2014-05-10 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations. This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the given differential equation with a known admitted group. The theory of differential invariants that is developed on an infinitesimal basis is elaborated in Chapter VII. The last chapter outlines the ways in which the methods of group analysis are used in special issues involving differential equations. This publication is a good source for students and specialists concerned with areas in which ordinary and partial differential equations play an important role.

Book Applications of Lie Groups to Differential Equations

Download or read book Applications of Lie Groups to Differential Equations written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

Book Numerical Methods for Partial Differential Equations

Download or read book Numerical Methods for Partial Differential Equations written by William F. Ames and published by Academic Press. This book was released on 2014-05-10 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements. This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.

Book The Kinematics of Mixing

Download or read book The Kinematics of Mixing written by J. M. Ottino and published by Cambridge University Press. This book was released on 1989 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: In spite of its universality, mixing is poorly understood and generally speaking, mixing problems are attacked on a case-by-case basis. This is the first book to present a unified treatment of the mixing of fluids from a kinematical viewpoint. The author's aim is to provide a conceptually clear basis from which to launch analysis and to facilitate an understanding of the numerous mixing problems encountered in nature and technology. After presenting the necessary background in kinematics and fluid dynamics, Professor Ottino considers various examples of dealing with necessary background in dynamical systems and chaos. The book assumes little previous knowledge of fluid dynamics and dynamical systems and can be used as a textbook by final-year undergraduates, graduate students and researchers in applied mathematics, engineering science, geophysics and physics who have an interest in fluid dynamics, continuum mechanics and dynamical systems. It is profusely illustrated in colour, with many line diagrams and half-tones. Systems which illustrate the most important concepts, many exercises and examples are included.

Book An Introduction to Theoretical Fluid Mechanics

Download or read book An Introduction to Theoretical Fluid Mechanics written by Stephen Childress and published by American Mathematical Soc.. This book was released on 2009-10-09 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an overview of classical topics in fluid dynamics, focusing on the kinematics and dynamics of incompressible inviscid and Newtonian viscous fluids, but also including some material on compressible flow. The topics are chosen to illustrate the mathematical methods of classical fluid dynamics. The book is intended to prepare the reader for more advanced topics of current research interest.

Book Numerical Analysis of Partial Differential Equations

Download or read book Numerical Analysis of Partial Differential Equations written by Jacques Louis Lions and published by Springer Science & Business Media. This book was released on 2011-06-07 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: S. Albertoni: Alcuni metodi di calcolo nella teoria della diffusione dei neutroni.- I. Babuska: Optimization and numerical stability in computations.- J.H. Bramble: Error estimates in elliptic boundary value problems.- G. Capriz: The numerical approach to hydrodynamic problems.- A. Dou: Energy inequalities in an elastic cylinder.- T. Doupont: On the existence of an iterative method for the solution of elliptic difference equation with an improved work estimate.- J. Douglas, J.R. Cannon: The approximation of harmonic and parabolic functions of half-spaces from interior data.- B.E. Hubbard: Error estimates in the fixed Membrane problem.- K. Jorgens: Calculation of the spectrum of a Schrödinger operator.- A. Lasota: Contingent equations and boundary value problems.- J.L. Lions: Réduction à des problèmes du type Cauchy-Kowalewska.- J.L. Lions: Problèmes aux limites non homogènes à données irrégulières; une méthode d’approximation.- J.L. Lions: Remarques sur l’approximation régularisée de problèmes aux limites.- W.V. Petryshyn: On the approximation-solvability of nonlinear functional equations in normed linear spaces.- P.A. Raviart: Approximation des équations d’évolution par des méthodes variationnelles.- M. Sibony, H. Brezis: Méthodes d’approximation et d’itération pour les operateurs monotones.- V. Thomee: Some topics in stability theory for partial difference operators.

Book Handbook of Fluid Dynamics

Download or read book Handbook of Fluid Dynamics written by Richard W. Johnson and published by CRC Press. This book was released on 2016-04-06 with total page 1544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Fluid Dynamics offers balanced coverage of the three traditional areas of fluid dynamics—theoretical, computational, and experimental—complete with valuable appendices presenting the mathematics of fluid dynamics, tables of dimensionless numbers, and tables of the properties of gases and vapors. Each chapter introduces a different fluid dynamics topic, discusses the pertinent issues, outlines proven techniques for addressing those issues, and supplies useful references for further research. Covering all major aspects of classical and modern fluid dynamics, this fully updated Second Edition: Reflects the latest fluid dynamics research and engineering applications Includes new sections on emerging fields, most notably micro- and nanofluidics Surveys the range of numerical and computational methods used in fluid dynamics analysis and design Expands the scope of a number of contemporary topics by incorporating new experimental methods, more numerical approaches, and additional areas for the application of fluid dynamics Handbook of Fluid Dynamics, Second Edition provides an indispensable resource for professionals entering the field of fluid dynamics. The book also enables experts specialized in areas outside fluid dynamics to become familiar with the field.

Book Energy Methods in Continuum Mechanics

Download or read book Energy Methods in Continuum Mechanics written by S.N. Antontsev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Workshop Energy Methods for Free Boundary Problems in Continuum Mechanics, held in Oviedo, Spain, from March 21 to March 23, 1994. It is well known that the conservation laws and the constitutive equations of Continuum Mechanics lead to complicated coupled systems of partial differential equations to which, as a rule, one fails to apply the techniques usually employed in the studies of scalar uncoupled equations such as, for instance, the maximum principle. The study of the qualitative behaviour of solutions of the systems re quires different techniques, among others, the so called, Energy Methods where the properties of some integral of a nonnegative function of one or several unknowns allow one to arrive at important conclusions on the envolved unknowns. This vol ume presents the state of the art in such a technique. A special attention is paid to the class of Free Boundary Problems. The organizers are pleased to thank the European Science Foundation (Pro gram on Mathematical treatment of free boundary problems), the DGICYT (Spain), the FICYT (Principado de Asturias, Spain) and the Universities of Oviedo and Complutense de Madrid for their generous financial support. Finally, we wish to thank Kluwer Academic Publishers for the facilities received for the publication of these Proceedings.

Book Grenzschichtforschung Boundary Layer Research

Download or read book Grenzschichtforschung Boundary Layer Research written by Heinrich Görtler and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: Der BeschluB des Generalrats der Internationalen Union fill Theo retische und Angewandte Mechanik (IUTAM), ein Symposium tiber Grenzschichtforschung vorzubereiten, war von dem Wunsch getragen, Wissenschaftlern aus aller Welt, die in eigenen Arbeiten zu den neueren Fortschritten auf diesem wichtigen Gebiet der Stromungsmechanik wesentlich beigetragen haben, zu grtindlichen Diskussionen Gelegenheit zu geben. Die grundsatzlichen Probleme der Grenzschichtforschung soUten bei der Aussprache im V ordergrund stehen, die technischen An wendungen muBten im Hintergrund bleiben. Da eine echte Diskussion nur in einem relativ kleinen Kreis moglich ist, hat das Wissenschaftliche Komitee den Kreis der Teilnehmer be schrankt, dabei aber nach Moglichkeit Vertreter aus allen an den Fort schritten der Grenzschichtforschung beteiligten Nationen zusammenge fUhrt. Die Teilnehmer wurden in Beratungen des Wissenschaftlichen Komitees ausgewahlt und entweder zur Erstattung eines allgemeinen oder eines speziellen Berichtes eingeladen bzw. zur Teilnahme an den Diskussionsveranstaltungen aufgefordert. Das Ergebnis dieser Tagung legen wir hiermit vor. 1m Druck sind aIle jene Fragen und Bemerkungen aus den Diskussionen weggelassen wor den, die sich durch das V orliegen des voUen V ortragstextes in diesem Buch von selbst erledigen, bzw. die durch nachtragliche Bearbeitung des Manuskriptes von den Autoren beriicksichtigt worden sind. Wir empfinden es mit Dank als eine Ehrung, daB die erste Veranstal tung der IUTAM in Deutschland die Grenzschichtforschung behandelt und damit das Gedenken an LUDWIG PRANDTL wachhalt, den Begriinder der Grenzschichtforschung und den Forderer der modernen Stromungs forschung.

Book Three Dimensional Navier Stokes Equations for Turbulence

Download or read book Three Dimensional Navier Stokes Equations for Turbulence written by Luigi C. Berselli and published by Academic Press. This book was released on 2021-03-10 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three-Dimensional Navier-Stokes Equations for Turbulence provides a rigorous but still accessible account of research into local and global energy dissipation, with particular emphasis on turbulence modeling. The mathematical detail is combined with coverage of physical terms such as energy balance and turbulence to make sure the reader is always in touch with the physical context. All important recent advancements in the analysis of the equations, such as rigorous bounds on structure functions and energy transfer rates in weak solutions, are addressed, and connections are made to numerical methods with many practical applications. The book is written to make this subject accessible to a range of readers, carefully tackling interdisciplinary topics where the combination of theory, numerics, and modeling can be a challenge. - Includes a comprehensive survey of modern reduced-order models, including ones for data assimilation - Includes a self-contained coverage of mathematical analysis of fluid flows, which will act as an ideal introduction to the book for readers without mathematical backgrounds - Presents methods and techniques in a practical way so they can be rapidly applied to the reader's own work

Book Elements Of Fluid Dynamics

Download or read book Elements Of Fluid Dynamics written by Guido Buresti and published by World Scientific Publishing Company. This book was released on 2012-06-26 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elements of Fluid Dynamics is intended to be a basic textbook, useful for undergraduate and graduate students in different fields of engineering, as well as in physics and applied mathematics. The main objective of the book is to provide an introduction to fluid dynamics in a simultaneously rigorous and accessible way, and its approach follows the idea that both the generation mechanisms and the main features of the fluid dynamic loads can be satisfactorily understood only after the equations of fluid motion and all their physical and mathematical implications have been thoroughly assimilated. Therefore, the complete equations of motion of a compressible viscous fluid are first derived and their physical and mathematical aspects are thoroughly discussed. Subsequently, the necessity of simplified treatments is highlighted, and a detailed analysis is made of the assumptions and range of applicability of the incompressible flow model, which is then adopted for most of the rest of the book. Furthermore, the role of the generation and dynamics of vorticity on the development of different flows is emphasized, as well as its influence on the characteristics, magnitude and predictability of the fluid dynamic loads acting on moving bodies.The book is divided into two parts which differ in target and method of utilization. The first part contains the fundamentals of fluid dynamics that are essential for any student new to the subject. This part of the book is organized in a strictly sequential way, i.e. each chapter is assumed to be carefully read and studied before the next one is tackled, and its aim is to lead the reader in understanding the origin of the fluid dynamic forces on different types of bodies. The second part of the book is devoted to selected topics that may be of more specific interest to different students. In particular, some theoretical aspects of incompressible flows are first analysed and classical applications of fluid dynamics such as the aerodynamics of airfoils, wings and bluff bodies are then described. The one-dimensional treatment of compressible flows is finally considered, together with its application to the study of the motion in ducts.

Book An Introduction to the Mechanics of Fluids

Download or read book An Introduction to the Mechanics of Fluids written by C. Truesdell and published by Springer Science & Business Media. This book was released on 2010-10-05 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compact, moderately general book which encompasses many fluid models of current interest...The book is written very clearly and contains a large number of exercises and their solutions. The level of mathematics is that commonly taught to undergraduates in mathematics departments.. —Mathematical Reviews The book should be useful for graduates and researchers not only in applied mathematics and mechanical engineering but also in advanced materials science and technology...Each public scientific library as well as hydrodynamics hand libraries should own this timeless book...Everyone who decides to buy this book can be sure to have bought a classic of science and the heritage of an outstanding scientist. —Silikáty All applied mathematicians, mechanical engineers, aerospace engineers, and engineering mechanics graduates and researchers will find the book an essential reading resource for fluids. —Simulation News Europe

Book Handbook of Linear Partial Differential Equations for Engineers and Scientists

Download or read book Handbook of Linear Partial Differential Equations for Engineers and Scientists written by Andrei D. Polyanin and published by CRC Press. This book was released on 2015-12-23 with total page 1623 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition contains nearly 4,000 linear partial differential equations (PDEs) with solutions as well as analytical, symbolic, and numerical methods for solving linear equations. First-, second-, third-, fourth-, and higher-order linear equations and systems of coupled equations are considered. Equations of parabolic, mixed, and other types are discussed. New linear equations, exact solutions, transformations, and methods are described. Formulas for effective construction of solutions are given. Boundary value and eigenvalue problems are addressed. Symbolic and numerical methods for solving PDEs with Maple, Mathematica, and MATLAB are explored.