Applications of Lie Groups to Difference Equations

Applications of Lie Groups to Difference Equations
Author: Vladimir Dorodnitsyn
Publisher: CRC Press
Total Pages: 344
Release: 2010-12-01
Genre: Mathematics
ISBN: 9781420083101
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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

Applications of Lie Groups to Differential Equations

Applications of Lie Groups to Differential Equations
Author: Peter J. Olver
Publisher: Springer Science & Business Media
Total Pages: 548
Release: 1993
Genre: Language Arts & Disciplines
ISBN: 9780387950006
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A solid introduction to applications of Lie groups to differential equations which have proved to be useful in practice. The computational methods are presented such that graduates and researchers can readily learn to use them. Following an exposition of the applications, the book develops the underlying theory, with many of the topics presented in a novel way, emphasising explicit examples and computations. Further examples, as well as new theoretical developments, appear in the exercises at the end of each chapter.

CRC Handbook of Lie Group Analysis of Differential Equations

CRC Handbook of Lie Group Analysis of Differential Equations
Author: Nail H. Ibragimov
Publisher: CRC Press
Total Pages: 570
Release: 1994-11-28
Genre: Mathematics
ISBN: 9780849328640
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Volume 2 offers a unique blend of classical results of Sophus Lie with new, modern developments and numerous applications which span a period of more than 100 years. As a result, this reference is up to date, with the latest information on the group theoretic methods used frequently in mathematical physics and engineering. Volume 2 is divided into three parts. Part A focuses on relevant definitions, main algorithms, group classification schemes for partial differential equations, and multifaceted possibilities offered by Lie group theoretic philosophy. Part B contains the group analysis of a variety of mathematical models for diverse natural phenomena. It tabulates symmetry groups and solutions for linear equations of mathematical physics, classical field theory, viscous and non-Newtonian fluids, boundary layer problems, Earth sciences, elasticity, plasticity, plasma theory (Vlasov-Maxwell equations), and nonlinear optics and acoustics. Part C offers an English translation of Sophus Lie's fundamental paper on the group classification and invariant solutions of linear second-order equations with two independent variables. This will serve as a concise, practical guide to the group analysis of partial differential equations.

CRC Handbook of Lie Group Analysis of Differential Equations

CRC Handbook of Lie Group Analysis of Differential Equations
Author: Nail H. Ibragimov
Publisher: CRC Press
Total Pages: 572
Release: 1995-10-24
Genre: Mathematics
ISBN: 9780849394195
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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.

Applications of Lie's Theory of Ordinary and Partial Differential Equations

Applications of Lie's Theory of Ordinary and Partial Differential Equations
Author: L Dresner
Publisher: CRC Press
Total Pages: 242
Release: 1998-01-01
Genre: Science
ISBN: 9781420050783
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Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.

Symmetry Methods for Differential Equations

Symmetry Methods for Differential Equations
Author: Peter Ellsworth Hydon
Publisher: Cambridge University Press
Total Pages: 230
Release: 2000-01-28
Genre: Mathematics
ISBN: 9780521497862
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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.

Symmetries, Differential Equations and Applications

Symmetries, Differential Equations and Applications
Author: Victor G. Kac
Publisher: Springer
Total Pages: 199
Release: 2018-11-04
Genre: Mathematics
ISBN: 3030013766
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Based on the third International Conference on Symmetries, Differential Equations and Applications (SDEA-III), this proceedings volume highlights recent important advances and trends in the applications of Lie groups, including a broad area of topics in interdisciplinary studies, ranging from mathematical physics to financial mathematics. The selected and peer-reviewed contributions gathered here cover Lie theory and symmetry methods in differential equations, Lie algebras and Lie pseudogroups, super-symmetry and super-integrability, representation theory of Lie algebras, classification problems, conservation laws, and geometrical methods. The SDEA III, held in honour of the Centenary of Noether’s Theorem, proven by the prominent German mathematician Emmy Noether, at Istanbul Technical University in August 2017 provided a productive forum for academic researchers, both junior and senior, and students to discuss and share the latest developments in the theory and applications of Lie symmetry groups. This work has an interdisciplinary appeal and will be a valuable read for researchers in mathematics, mechanics, physics, engineering, medicine and finance.

A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods

A Survey of Lie Groups and Lie Algebras with Applications and Computational Methods
Author: Johan G. F. Belinfante
Publisher: SIAM
Total Pages: 175
Release: 1989-01-01
Genre: Mathematics
ISBN: 9781611971330
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Introduces the concepts and methods of the Lie theory in a form accessible to the non-specialist by keeping mathematical prerequisites to a minimum. Although the authors have concentrated on presenting results while omitting most of the proofs, they have compensated for these omissions by including many references to the original literature. Their treatment is directed toward the reader seeking a broad view of the subject rather than elaborate information about technical details. Illustrations of various points of the Lie theory itself are found throughout the book in material on applications. In this reprint edition, the authors have resisted the temptation of including additional topics. Except for correcting a few minor misprints, the character of the book, especially its focus on classical representation theory and its computational aspects, has not been changed.

CRC Handbook of Lie Group Analysis of Differential Equations

CRC Handbook of Lie Group Analysis of Differential Equations
Author: Nail H. Ibragimov
Publisher: CRC Press
Total Pages: 452
Release: 1993-10-20
Genre: Mathematics
ISBN: 9780849344886
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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 the modern group analysis and addresses issues to both beginners and experienced researchers in the application of Lie group methods.