Form Symmetries And Reduction Of Order In Difference Equations

Author : Hassan Sedaghat
Publisher : CRC Press
Page : 327 pages
File Size : 42,7 Mb
Release : 2011-05-24
Category : Mathematics
ISBN : 9781439807606

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Form Symmetries and Reduction of Order in Difference Equations by Hassan Sedaghat Pdf

Form Symmetries and Reduction of Order in Difference Equations presents a new approach to the formulation and analysis of difference equations in which the underlying space is typically an algebraic group. In some problems and applications, an additional algebraic or topological structure is assumed in order to define equations and obtain significant results about them. Reflecting the author’s past research experience, the majority of examples involve equations in finite dimensional Euclidean spaces. The book first introduces difference equations on groups, building a foundation for later chapters and illustrating the wide variety of possible formulations and interpretations of difference equations that occur in concrete contexts. The author then proposes a systematic method of decomposition for recursive difference equations that uses a semiconjugate relation between maps. Focusing on large classes of difference equations, he shows how to find the semiconjugate relations and accompanying factorizations of two difference equations with strictly lower orders. The final chapter goes beyond semiconjugacy by extending the fundamental ideas based on form symmetries to nonrecursive difference equations. With numerous examples and exercises, this book is an ideal introduction to an exciting new domain in the area of difference equations. It takes a fresh and all-inclusive look at difference equations and develops a systematic procedure for examining how these equations are constructed and solved.

Author : Hassan Sedaghat
Publisher : CRC Press
Page : 322 pages
File Size : 51,8 Mb
Release : 2011-05-24
Category : Mathematics
ISBN : 9781439807644

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Form Symmetries and Reduction of Order in Difference Equations by Hassan Sedaghat Pdf

Form Symmetries and Reduction of Order in Difference Equations presents a new approach to the formulation and analysis of difference equations in which the underlying space is typically an algebraic group. In some problems and applications, an additional algebraic or topological structure is assumed in order to define equations and obtain significa

Author : Hans Stephani
Publisher : Cambridge University Press
Page : 278 pages
File Size : 41,6 Mb
Release : 1989
Category : Differential equations
ISBN : 0521366895

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Differential Equations by Hans Stephani Pdf

This book provides an introduction to the theory and application of the solution to differential equations using symmetries, a technique of great value in mathematics and the physical sciences. It will apply to graduate students in physics, applied mathematics, and engineering.

Author : George Bluman,Stephen Anco
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 54,9 Mb
Release : 2008-01-10
Category : Mathematics
ISBN : 9780387216492

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Symmetry and Integration Methods for Differential Equations by George Bluman,Stephen Anco Pdf

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.

Author : David Blázquez-Sanz,Juan José Morales Ruiz,Jesús Rodríguez Lombardero
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 51,7 Mb
Release : 2011-01-01
Category : Mathematics
ISBN : 9780821882429

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Symmetries and Related Topics in Differential and Difference Equations by David Blázquez-Sanz,Juan José Morales Ruiz,Jesús Rodríguez Lombardero Pdf

Author : Willi-Hans Steeb
Publisher : World Scientific
Page : 188 pages
File Size : 52,7 Mb
Release : 1993-06-04
Category : Science
ISBN : 9789814504362

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Invertible Point Transformations and Nonlinear Differential Equations by Willi-Hans Steeb Pdf

The invertible point transformation is a powerful tool in the study of nonlinear differential and difference equations. This book gives a comprehensive introduction to this technique. Ordinary and partial differential equations are studied with this approach. The book also covers nonlinear difference equations. The connections with Lie symmetries, the Painlevé property, first integrals and the Cartan equivalence method are discussed in detail. Most of the evaluations are checked with the computer language REDUCE; the book includes 30 REDUCE programs. A short introduction to the jet bundle formalism is given. Contents:First-Order Ordinary Differential EquationSecond-Order Ordinary Differential EquationsThird-Order Differential EquationsLie Point SymmetriesFirst Integrals and Differential EquationCartan Equivalence MethodPainlevé Test and LinearizationPainlevé Test and Partial Differential EquationsPartial Differential EquationsDifference EquationsREDUCE ProgramsJet Bundle Formalism Readership: Mathematicians, physicists and engineers. keywords:Nonlinear Differential Equations;Invertible Point Transformation;Lie Point Symmetries;Painleve Test;Jet Bundle Formalism “The text is well written, and fairly elementary from a mathematical standpoint. The concepts are clearly illustrated; there are numerous examples of interest to applied mathematicians and physicists.” SIAM Review

Author : Peter J. Olver
Publisher : Cambridge University Press
Page : 546 pages
File Size : 41,7 Mb
Release : 1995-06-30
Category : Mathematics
ISBN : 0521478111

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Equivalence, Invariants and Symmetry by Peter J. Olver Pdf

Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

Author : Peter E. Hydon
Publisher : Cambridge University Press
Page : 223 pages
File Size : 55,5 Mb
Release : 2014-08-07
Category : Mathematics
ISBN : 9781139991704

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Difference Equations by Differential Equation Methods by Peter E. Hydon Pdf

Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.

Author : Peter Ellsworth Hydon
Publisher : Cambridge University Press
Page : 230 pages
File Size : 46,7 Mb
Release : 2000-01-28
Category : Mathematics
ISBN : 0521497868

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Symmetry Methods for Differential Equations by Peter Ellsworth Hydon Pdf

This book is a straightforward introduction to the subject of symmetry methods for solving differential equations, and is aimed at applied mathematicians, physicists, and engineers. The presentation is informal, using many worked examples to illustrate the main symmetry methods. It is written at a level suitable for postgraduates and advanced undergraduates, and is designed to enable the reader to master the main techniques quickly and easily.The book contains some methods that have not previously appeared in a text. These include methods for obtaining discrete symmetries and integrating factors.

Author : James Eells,Andrea Ratto
Publisher : Princeton University Press
Page : 238 pages
File Size : 55,7 Mb
Release : 1993
Category : Mathematics
ISBN : 069110249X

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Harmonic Maps and Minimal Immersions with Symmetries by James Eells,Andrea Ratto Pdf

The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.

Author : George W. Bluman,Sukeyuki Kumei
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 51,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475743074

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Symmetries and Differential Equations by George W. Bluman,Sukeyuki Kumei Pdf

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.

Author : Leonard C. Maximon
Publisher : Springer
Page : 162 pages
File Size : 50,5 Mb
Release : 2016-04-18
Category : Science
ISBN : 9783319297361

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Differential and Difference Equations by Leonard C. Maximon Pdf

This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, reduction of order, Laplace transforms and generating functions - bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green’s functions and the associated initial and boundary conditions is presented for differential and difference equations of both arbitrary and second order. A dictionary of difference equations with polynomial coefficients provides a unique compilation of second order difference equations obeyed by the special functions of mathematical physics. Appendices augmenting the text include, in particular, a proof of Cramer’s rule, a detailed consideration of the role of the superposition principal in the Green’s function, and a derivation of the inverse of Laplace transforms and generating functions of particular use in the solution of second order linear differential and difference equations with linear coefficients.

Author : Decio Levi,Peter Olver,Zora Thomova,Pavel Winternitz
Publisher : Cambridge University Press
Page : 361 pages
File Size : 44,8 Mb
Release : 2011-06-23
Category : Mathematics
ISBN : 9781139493840

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Symmetries and Integrability of Difference Equations by Decio Levi,Peter Olver,Zora Thomova,Pavel Winternitz Pdf

A comprehensive introduction to the subject suitable for graduate students and researchers. This book is also an up-to-date survey of the current state of the art and thus will serve as a valuable reference for specialists in the field.

Author : Calvin Ahlbrandt,A.C. Peterson
Publisher : Springer Science & Business Media
Page : 384 pages
File Size : 47,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475724677

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Discrete Hamiltonian Systems by Calvin Ahlbrandt,A.C. Peterson Pdf

This book should be accessible to students who have had a first course in matrix theory. The existence and uniqueness theorem of Chapter 4 requires the implicit function theorem, but we give a self-contained constructive proof ofthat theorem. The reader willing to accept the implicit function theorem can read the book without an advanced calculus background. Chapter 8 uses the Moore-Penrose pseudo-inverse, but is accessible to students who have facility with matrices. Exercises are placed at those points in the text where they are relevant. For U. S. universities, we intend for the book to be used at the senior undergraduate level or beginning graduate level. Chapter 2, which is on continued fractions, is not essential to the material of the remaining chapters, but is intimately related to the remaining material. Continued fractions provide closed form representations of the extreme solutions of some discrete matrix Riccati equations. Continued fractions solution methods for Riccati difference equations provide an approach analogous to series solution methods for linear differential equations. The book develops several topics which have not been available at this level. In particular, the material of the chapters on continued fractions (Chapter 2), symplectic systems (Chapter 3), and discrete variational theory (Chapter 4) summarize recent literature. Similarly, the material on transforming Riccati equations presented in Chapter 3 gives a self-contained unification of various forms of Riccati equations. Motivation for our approach to difference equations came from the work of Harris, Vaughan, Hartman, Reid, Patula, Hooker, Erbe & Van, and Bohner.

Author : Peter J. Olver
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468402742

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Applications of Lie Groups to Differential Equations by Peter J. Olver Pdf

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.