Symmetries And Differential Equations
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Symmetries And Differential Equations
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Author : George W. Bluman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Symmetries And Differential Equations written by George W. Bluman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
A major portion of this book discusses work which has appeared since the publication of the book Similarity Methods for Differential Equations, Springer-Verlag, 1974, by the first author and J.D. Cole. The present book also includes a thorough and comprehensive treatment of Lie groups of tranformations and their various uses for solving ordinary and partial differential equations. No knowledge of group theory is assumed. Emphasis is placed on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This book should be particularly suitable for physicists, applied mathematicians, and engineers. Almost all of the examples are taken from physical and engineering problems including those concerned with heat conduction, wave propagation, and fluid flows. A preliminary version was used as lecture notes for a two-semester course taught by the first author at the University of British Columbia in 1987-88 to graduate and senior undergraduate students in applied mathematics and physics. Chapters 1 to 4 encompass basic material. More specialized topics are covered in Chapters 5 to 7.
Symmetry And Integration Methods For Differential Equations
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Author : George Bluman
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-07-10
Symmetry And Integration Methods For Differential Equations written by George Bluman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-10 with Mathematics categories.
This text discusses Lie groups of transformations and basic symmetry methods for solving ordinary and partial differential equations. It places emphasis on explicit computational algorithms to discover symmetries admitted by differential equations and to construct solutions resulting from symmetries. This new edition covers contact transformations, Lie-B cklund transformations, and adjoints and integrating factors for ODEs of arbitrary order.
Symmetry Methods For Differential Equations
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Author : Peter E. Hydon
language : en
Publisher: Cambridge University Press
Release Date : 2000-02-13
Symmetry Methods For Differential Equations written by Peter E. Hydon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-13 with Mathematics categories.
A good working knowledge of symmetry methods is very valuable for those working with mathematical models. This book is a straightforward introduction to the subject for applied mathematicians, physicists, and engineers. The informal presentation uses many worked examples to illustrate the major symmetry methods. Written at a level suitable for postgraduates and advanced undergraduates, the text will enable readers to master the main techniques quickly and easily. The book contains some methods not previously published in a text, including those methods for obtaining discrete symmetries and integrating factors.
Applications Of Symmetry Methods To Partial Differential Equations
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Author : George W. Bluman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-30
Applications Of Symmetry Methods To Partial Differential Equations written by George W. Bluman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-30 with Mathematics categories.
This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.
Applications Of Lie Groups To Differential Equations
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Author : Peter J. Olver
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Lie Groups To Differential Equations written by Peter J. Olver and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Differential Equations
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Author : Hans Stephani
language : en
Publisher: Cambridge University Press
Release Date : 1989
Differential Equations written by Hans Stephani and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
In many branches of physics, mathematics, and engineering, solving a problem means solving a set of ordinary or partial differential equations. Nearly all methods of constructing closed form solutions rely on symmetries. The emphasis in this text is on how to find and use the symmetries; this is supported by many examples and more than 100 exercises. This book will form an introduction accessible to beginning graduate students in physics, applied mathematics, and engineering. Advanced graduate students and researchers in these disciplines will find the book a valuable reference.
Lie Symmetry Analysis Of Fractional Differential Equations
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Author : Mir Sajjad Hashemi
language : en
Publisher: CRC Press
Release Date : 2020-07-09
Lie Symmetry Analysis Of Fractional Differential Equations written by Mir Sajjad Hashemi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-09 with Mathematics categories.
The trajectory of fractional calculus has undergone several periods of intensive development, both in pure and applied sciences. During the last few decades fractional calculus has also been associated with the power law effects and its various applications. It is a natural to ask if fractional calculus, as a nonlocal calculus, can produce new results within the well-established field of Lie symmetries and their applications. In Lie Symmetry Analysis of Fractional Differential Equations the authors try to answer this vital question by analyzing different aspects of fractional Lie symmetries and related conservation laws. Finding the exact solutions of a given fractional partial differential equation is not an easy task, but is one that the authors seek to grapple with here. The book also includes generalization of Lie symmetries for fractional integro differential equations. Features Provides a solid basis for understanding fractional calculus, before going on to explore in detail Lie Symmetries and their applications Useful for PhD and postdoc graduates, as well as for all mathematicians and applied researchers who use the powerful concept of Lie symmetries Filled with various examples to aid understanding of the topics
Applications Of Lie Groups To Difference Equations
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Author : Vladimir Dorodnitsyn
language : en
Publisher: CRC Press
Release Date : 2010-12-01
Applications Of Lie Groups To Difference Equations written by Vladimir Dorodnitsyn and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-01 with Mathematics categories.
Intended for researchers, numerical analysts, and graduate students in various fields of applied mathematics, physics, mechanics, and engineering sciences, Applications of Lie Groups to Difference Equations is the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. A guide to methods
Symmetries And Conservation Laws For Differential Equations Of Mathematical Physics
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Author : A. V. Bocharov Aleksandr Mikhaĭlovich Vinogradov
language : en
Publisher: American Mathematical Soc.
Release Date :
Symmetries And Conservation Laws For Differential Equations Of Mathematical Physics written by A. V. Bocharov Aleksandr Mikhaĭlovich Vinogradov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
This book presents developments in the geometric approach to nonlinear partial differential equations (PDEs). The expositions discuss the main features of the approach, and the theory of symmetries and the conservation laws based on it. The book combines rigorous mathematics with concrete examples. Nontraditional topics, such as the theory of nonlocal symmetries and cohomological theory of conservation laws, are also included. The volume is largely self-contained and includes detailed motivations, extensive examples and exercises, and careful proofs of all results. Readers interested in learning the basics of applications of symmetry methods to differential equations of mathematical physics will find the text useful. Experts will also find it useful as it gathers many results previously only available in journals.
Introduction To Symmetry Analysis Paperback With Cd Rom
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Author : Brian Cantwell
language : en
Publisher: Cambridge University Press
Release Date : 2002-09-23
Introduction To Symmetry Analysis Paperback With Cd Rom written by Brian Cantwell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-23 with Mathematics categories.
An introduction to symmetry analysis for graduate students in science, engineering and applied mathematics.