Symmetry Analysis Of Differential Equations
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Symmetry Analysis Of Differential Equations With Mathematica
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Author : Gerd Baumann
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-04-20
Symmetry Analysis Of Differential Equations With Mathematica written by Gerd Baumann 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 2000-04-20 with Mathematics categories.
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.
Introduction To Symmetry Analysis
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Author : Brian J. Cantwell
language : en
Publisher: Cambridge University Press
Release Date : 2002-09-26
Introduction To Symmetry Analysis written by Brian J. 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 2002-09-26 with Mathematics categories.
Symmetry Analysis Of Differential Equations
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Author : Daniel J. Arrigo
language : en
Publisher:
Release Date : 2015
Symmetry Analysis Of Differential Equations written by Daniel J. Arrigo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Differential equations, Partial categories.
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.
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
Symmetry Analysis Of Differential Equations With Mathematica
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Author : Gerd Baumann
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Symmetry Analysis Of Differential Equations With Mathematica written by Gerd Baumann 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 2013-11-21 with Mathematics categories.
The purpose of this book is to provide the reader with a comprehensive introduction to the applications of symmetry analysis to ordinary and partial differential equations. The theoretical background of physics is illustrated by modem methods of computer algebra. The presentation of the material in the book is based on Mathematica 3.0 note books. The entire printed version of this book is available on the accompanying CD. The text is presented in such a way that the reader can interact with the calculations and experiment with the models and methods. Also contained on the CD is a package called MathLie-in honor of Sophus Lie---carrying out the calculations automatically. The application of symmetry analysis to problems from physics, mathematics, and en gineering is demonstrated by many examples. The study of symmetries of differential equations is an old subject. Thanks to Sophus Lie we today have available to us important information on the behavior of differential equations. Symmetries can be used to find exact solutions. Symmetries can be applied to verify and to develop numerical schemes. They can provide conservation laws for differential equations. The theory presented here is based on Lie, containing improve ments and generalizations made by later mathematicians who rediscovered and used Lie's work. The presentation of Lie's theory in connection with Mathematica is novel and vitalizes an old theory. The extensive symbolic calculations necessary under Lie's theory are supported by MathLie, a package written in Mathematica.
Symmetries And Applications Of Differential Equations
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Author : Albert C. J. Luo
language : en
Publisher: Springer Nature
Release Date : 2021-12-14
Symmetries And Applications Of Differential Equations written by Albert C. J. Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-14 with Mathematics categories.
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.
Introduction To Symmetry Analysis
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Author : Brian J. Cantwell
language : en
Publisher: Cambridge University Press
Release Date : 2002-09-23
Introduction To Symmetry Analysis written by Brian J. 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.
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.
Symmetry Analysis Of Differential Equations From A Geometric Point Of View
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Author : Thomas Hartl
language : en
Publisher:
Release Date : 1998
Symmetry Analysis Of Differential Equations From A Geometric Point Of View written by Thomas Hartl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Analytical Methods In Differential Equations
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Author : Sergey V. Meleshko
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-02-17
Analytical Methods In Differential Equations written by Sergey V. Meleshko and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-17 with Mathematics categories.
The book compiles papers presented at the International Conference 'Advances in Applications of Analytical Methods in Solving Differential Equations', held in honour of Academician Lev V. Ovsiannikov’s 105th birthday anniversary. This collection reflects his extensive contributions to the theory of differential equations, modelling, and the application of analytical methods. In addition to classical methods such as analytical integration of systems of equations and their applications in various fields of Science and Engineering, the book explores new areas of research. This includes the application of group analysis to novel mathematical models and nonlinear problems, particularly equations with nonlocal terms (symmetries of difference and differential equations, as well as fractional differential equations). One of the notable contributions in the book is the development of a Hamiltonian approach for delay differential equations, representing a novel area of research that has not been previously explored. The book is anticipated to appeal to a broad audience of experts in applied mathematics, fluid dynamics, and modelling, as well as to young scientists and graduate students interested in the analysis of nonlinear equations.
Approximate And Renormgroup Symmetries
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Author : N. Kh. Ibragimov
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-11-14
Approximate And Renormgroup Symmetries written by N. Kh. Ibragimov 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 2009-11-14 with Mathematics categories.
"Approximate and Renormgroup Symmetries" deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. Dr. N.H. Ibragimov is a professor at the Department of Mathematics and Science, Research Centre ALGA, Sweden. He is widely regarded as one of the world's foremost experts in the field of symmetry analysis of differential equations; Dr. V. F. Kovalev is a leading scientist at the Institute for Mathematical Modeling, Russian Academy of Science, Moscow.