Symmetry Analysis Of Differential Equations

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Symmetry Analysis of Differential Equations

Daniel J. Arrigo
Symmetry Analysis of Differential Equations Book PDF

Author : Daniel J. Arrigo
Publisher : John Wiley & Sons
Page : 190 pages
File Size : 45,9 Mb
Release : 2015-01-20
Category : Mathematics
ISBN : 9781118721407

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Symmetry Analysis of Differential Equations by Daniel J. Arrigo Pdf

A self-contained introduction to the methods and techniques of symmetry analysis used to solve ODEs and PDEs Symmetry Analysis of Differential Equations: An Introduction presents an accessible approach to the uses of symmetry methods in solving both ordinary differential equations (ODEs) and partial differential equations (PDEs). Providing comprehensive coverage, the book fills a gap in the literature by discussing elementary symmetry concepts and invariance, including methods for reducing the complexity of ODEs and PDEs in an effort to solve the associated problems. Thoroughly class-tested, the author presents classical methods in a systematic, logical, and well-balanced manner. As the book progresses, the chapters graduate from elementary symmetries and the invariance of algebraic equations, to ODEs and PDEs, followed by coverage of the nonclassical method and compatibility. Symmetry Analysis of Differential Equations: An Introduction also features: Detailed, step-by-step examples to guide readers through the methods of symmetry analysis End-of-chapter exercises, varying from elementary to advanced, with select solutions to aid in the calculation of the presented algorithmic methods Symmetry Analysis of Differential Equations: An Introduction is an ideal textbook for upper-undergraduate and graduate-level courses in symmetry methods and applied mathematics. The book is also a useful reference for professionals in science, physics, and engineering, as well as anyone wishing to learn about the use of symmetry methods in solving differential equations.

Symmetry Analysis of Differential Equations with Mathematica®

Gerd Baumann
Symmetry Analysis of Differential Equations with Mathematica Book PDF

Author : Gerd Baumann
Publisher : Springer Science & Business Media
Page : 532 pages
File Size : 42,9 Mb
Release : 2013-11-21
Category : Mathematics
ISBN : 9781461221104

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Symmetry Analysis of Differential Equations with Mathematica® by Gerd Baumann Pdf

The first book to explicitly use Mathematica so as to allow researchers and students to more easily compute and solve almost any kind of differential equation using Lie's theory. Previously time-consuming and cumbersome calculations are now much more easily and quickly performed using the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, will be of interest to a broad group of scientists, mathematicians and engineers involved in dealing with symmetry analysis of differential equations. Each section of the book starts with a theoretical discussion of the material, then shows the application in connection with Mathematica. The cross-platform CD-ROM contains Mathematica (version 3.0) notebooks which allow users to directly interact with the code presented within the book. In addition, the author's proprietary "MathLie" software is included, so users can readily learn to use this powerful tool in regard to performing algebraic computations.

Symmetry Methods for Differential Equations

Peter Ellsworth Hydon
Symmetry Methods for Differential Equations Book PDF

Author : Peter Ellsworth Hydon
Publisher : Cambridge University Press
Page : 230 pages
File Size : 41,6 Mb
Release : 2000-01-28
Category : Mathematics
ISBN : 0521497868

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Symmetry Methods for Differential Equations by Peter Ellsworth Hydon Pdf

An introduction to symmetry methods, informally written and aimed at applied mathematicians, physicists, and engineers.

Lie Symmetry Analysis of Fractional Differential Equations

Mir Sajjad Hashemi,Dumitru Baleanu
Lie Symmetry Analysis of Fractional Differential Equations Book PDF

Author : Mir Sajjad Hashemi,Dumitru Baleanu
Publisher : CRC Press
Page : 223 pages
File Size : 51,9 Mb
Release : 2020-07-09
Category : Mathematics
ISBN : 9781000068931

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Lie Symmetry Analysis of Fractional Differential Equations by Mir Sajjad Hashemi,Dumitru Baleanu Pdf

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

Introduction to Symmetry Analysis

Brian J. Cantwell
Introduction to Symmetry Analysis Book PDF

Author : Brian J. Cantwell
Publisher : Cambridge University Press
Page : 670 pages
File Size : 49,5 Mb
Release : 2002-09-23
Category : Mathematics
ISBN : 1139431714

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Introduction to Symmetry Analysis by Brian J. Cantwell Pdf

Symmetry analysis based on Lie group theory is the most important method for solving nonlinear problems aside from numerical computation. The method can be used to find the symmetries of almost any system of differential equations and the knowledge of these symmetries can be used to reduce the complexity of physical problems governed by the equations. This is a broad, self-contained, introduction to the basics of symmetry analysis for first and second year graduate students in science, engineering and applied mathematics. Mathematica-based software for finding the Lie point symmetries and Lie-Bäcklund symmetries of differential equations is included on a CD along with more than forty sample notebooks illustrating applications ranging from simple, low order, ordinary differential equations to complex systems of partial differential equations. MathReader 4.0 is included to let the user read the sample notebooks and follow the procedure used to find symmetries.

Symmetries and Applications of Differential Equations

Albert C. J. Luo,Rafail K. Gazizov
Symmetries and Applications of Differential Equations Book PDF

Author : Albert C. J. Luo,Rafail K. Gazizov
Publisher : Springer Nature
Page : 287 pages
File Size : 40,5 Mb
Release : 2021-12-14
Category : Mathematics
ISBN : 9789811646836

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Symmetries and Applications of Differential Equations by Albert C. J. Luo,Rafail K. Gazizov Pdf

This book is about Lie group analysis of differential equations for physical and engineering problems. The topics include: -- Approximate symmetry in nonlinear physical problems -- Complex methods for Lie symmetry analysis -- Lie group classification, Symmetry analysis, and conservation laws -- Conservative difference schemes -- Hamiltonian structure and conservation laws of three-dimensional linear elasticity -- Involutive systems of partial differential equations This collection of works is written in memory of Professor Nail H. Ibragimov (1939–2018). It could be used as a reference book in differential equations in mathematics, mechanical, and electrical engineering.

Symmetries and Differential Equations

George W. Bluman,Sukeyuki Kumei
Symmetries and Differential Equations Book PDF

Author : George W. Bluman,Sukeyuki Kumei
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 53,5 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.

Applications of Lie Groups to Differential Equations

Peter J. Olver
Applications of Lie Groups to Differential Equations Book PDF

Author : Peter J. Olver
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 51,9 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.

Lie Symmetry Analysis of Fractional Differential Equations

Mir Sajjad Hashemi,Dumitru Baleanu
Lie Symmetry Analysis of Fractional Differential Equations Book PDF

Author : Mir Sajjad Hashemi,Dumitru Baleanu
Publisher : CRC Press
Page : 223 pages
File Size : 46,8 Mb
Release : 2020-07-09
Category : Mathematics
ISBN : 9781000068931

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Lie Symmetry Analysis of Fractional Differential Equations by Mir Sajjad Hashemi,Dumitru Baleanu Pdf

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

Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics

W.I. Fushchich,W.M. Shtelen,N.I. Serov
Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics Book PDF

Author : W.I. Fushchich,W.M. Shtelen,N.I. Serov
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 52,5 Mb
Release : 2013-03-14
Category : Science
ISBN : 9789401731980

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Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics by W.I. Fushchich,W.M. Shtelen,N.I. Serov Pdf

by spin or (spin s = 1/2) field equations is emphasized because their solutions can be used for constructing solutions of other field equations insofar as fields with any spin may be constructed from spin s = 1/2 fields. A brief account of the main ideas of the book is presented in the Introduction. The book is largely based on the authors' works [55-109, 176-189, 13-16, 7*-14*,23*, 24*] carried out in the Institute of Mathematics, Academy of Sciences of the Ukraine. References to other sources is not intended to imply completeness. As a rule, only those works used directly are cited. The authors wish to express their gratitude to Academician Yu.A. Mitropoi sky, and to Academician of Academy of Sciences of the Ukraine O.S. Parasyuk, for basic support and stimulation over the course of many years; to our cowork ers in the Department of Applied Studies, LA. Egorchenko, R.Z. Zhdanov, A.G. Nikitin, LV. Revenko, V.L Lagno, and I.M. Tsifra for assistance with the manuscript.

Applications of Symmetry Methods to Partial Differential Equations

George W. Bluman,Alexei F. Cheviakov,Stephen Anco
Applications of Symmetry Methods to Partial Differential Equations Book PDF

Author : George W. Bluman,Alexei F. Cheviakov,Stephen Anco
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 49,7 Mb
Release : 2009-10-30
Category : Mathematics
ISBN : 9780387680286

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Applications of Symmetry Methods to Partial Differential Equations by George W. Bluman,Alexei F. Cheviakov,Stephen Anco Pdf

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.

CRC Handbook of Lie Group Analysis of Differential Equations

Nail H. Ibragimov
CRC Handbook of Lie Group Analysis of Differential Equations Book PDF

Author : Nail H. Ibragimov
Publisher : CRC Press
Page : 572 pages
File Size : 41,8 Mb
Release : 1995-10-24
Category : Mathematics
ISBN : 0849394198

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CRC Handbook of Lie Group Analysis of Differential Equations by Nail H. Ibragimov Pdf

Today Lie group theoretical approach to differential equations has been extended to new situations and has become applicable to the majority of equations that frequently occur in applied sciences. Newly developed theoretical and computational methods are awaiting application. Students and applied scientists are expected to understand these methods. Volume 3 and the accompanying software allow readers to extend their knowledge of computational algebra. Written by the world's leading experts in the field, this up-to-date sourcebook covers topics such as Lie-Bäcklund, conditional and non-classical symmetries, approximate symmetry groups for equations with a small parameter, group analysis of differential equations with distributions, integro-differential equations, recursions, and symbolic software packages. The text provides an ideal introduction to modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.

Symmetry and Integration Methods for Differential Equations

George Bluman,Stephen Anco
Symmetry and Integration Methods for Differential Equations Book PDF

Author : George Bluman,Stephen Anco
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 44,9 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.

Numerical Analysis or Numerical Method in Symmetry

Clemente Cesarano
Numerical Analysis or Numerical Method in Symmetry Book PDF

Author : Clemente Cesarano
Publisher : MDPI
Page : 194 pages
File Size : 42,5 Mb
Release : 2020-02-21
Category : Mathematics
ISBN : 9783039283729

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Numerical Analysis or Numerical Method in Symmetry by Clemente Cesarano Pdf

This Special Issue focuses mainly on techniques and the relative formalism typical of numerical methods and therefore of numerical analysis, more generally. These fields of study of mathematics represent an important field of investigation both in the field of applied mathematics and even more exquisitely in the pure research of the theory of approximation and the study of polynomial relations as well as in the analysis of the solutions of the differential equations both ordinary and partial derivatives. Therefore, a substantial part of research on the topic of numerical analysis cannot exclude the fundamental role played by approximation theory and some of the tools used to develop this research. In this Special Issue, we want to draw attention to the mathematical methods used in numerical analysis, such as special functions, orthogonal polynomials, and their theoretical tools, such as Lie algebra, to study the concepts and properties of some special and advanced methods, which are useful in the description of solutions of linear and nonlinear differential equations. A further field of investigation is dedicated to the theory and related properties of fractional calculus with its adequate application to numerical methods.

Differential Equations

Hans Stephani
Differential Equations Book PDF

Author : Hans Stephani
Publisher : Cambridge University Press
Page : 278 pages
File Size : 47,9 Mb
Release : 1989
Category : Mathematics
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 of differential equations using symmetries, a technique of great value in mathematics and the physical sciences. In many branches of physics, mathematics, and engineering, solving a problem means a set of ordinary or partial differential equations. Nearly all methods of constructing closed form solutions rely on symmetries. The theory and application of such methods have therefore attracted increasing attention in the last two decades. In this text the emphasis is on how to find and use the symmetries in different cases. Many examples are discussed, and the book includes 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 an invaluable reference.