Lie Theoretic Ode Numerical Analysis Mechanics And Differential Systems
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Lie Theoretic Ode Numerical Analysis Mechanics And Differential Systems
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Author : Robert Hermann
language : en
Publisher: Math-Sci Press
Release Date : 1994
Lie Theoretic Ode Numerical Analysis Mechanics And Differential Systems written by Robert Hermann and has been published by Math-Sci Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Interdisciplinary Mathematics Lie Theoretic Ode Numerical Analysis Mechanics And Differential Systems
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Author : Robert Hermann
language : en
Publisher:
Release Date : 1973
Interdisciplinary Mathematics Lie Theoretic Ode Numerical Analysis Mechanics And Differential Systems written by Robert Hermann and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Mathematical physics categories.
Algorithmic Lie Theory For Solving Ordinary Differential Equations
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Author : Fritz Schwarz
language : en
Publisher: CRC Press
Release Date : 2007-10-02
Algorithmic Lie Theory For Solving Ordinary Differential Equations written by Fritz Schwarz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-02 with Mathematics categories.
Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete proble
Crc Handbook Of Lie Group Analysis Of Differential Equations
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Author : Nail H. Ibragimov
language : en
Publisher: CRC Press
Release Date : 1994-11-28
Crc Handbook Of Lie Group Analysis Of Differential Equations written by Nail H. Ibragimov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-28 with Mathematics categories.
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.
Applications Of Lie S Theory Of Ordinary And Partial Differential Equations
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Author : L Dresner
language : en
Publisher: CRC Press
Release Date : 1998-01-01
Applications Of Lie S Theory Of Ordinary And Partial Differential Equations written by L Dresner and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Science categories.
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.
Group Theoretic Methods In Mechanics And Applied Mathematics
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Author : D.M. Klimov
language : en
Publisher: CRC Press
Release Date : 2002-08-15
Group Theoretic Methods In Mechanics And Applied Mathematics written by D.M. Klimov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-15 with Science categories.
Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. For the first time, this book gives the systematic group analysis of main postulates of classical and relativistic mechanics. The consistent presentation of Lie group theory is illustrated by plentiful examples. Symmetries and conservation laws of differential equations are studied. Specific equations and problems of mechanics and physics are considered, and exact solutions are given for the following equations: dynamics of rigid body, heat transfer, wave, hydrodynamics, Thomas-Fermi and more. The author pays particular attention to the application of group analysis to developing asymptotic methods of applied mathematics in problems with small parameter. The methods are used to solve basic equations (Van Der Pol's equation, Duffing equation, etc.) encountered in the theory of nonlinear oscillations. This book is intended for a wide range of scientists, engineers and students in the fields of applied mathematics, mechanics and physics.
Differential Equations Mechanics And Computation
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Author : Richard S. Palais
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-11-13
Differential Equations Mechanics And Computation written by Richard S. Palais 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 2009-11-13 with Mathematics categories.
This book provides a conceptual introduction to the theory of ordinary differential equations, concentrating on the initial value problem for equations of evolution and with applications to the calculus of variations and classical mechanics, along with a discussion of chaos theory and ecological models. It has a unified and visual introduction to the theory of numerical methods and a novel approach to the analysis of errors and stability of various numerical solution algorithms based on carefully chosen model problems. While the book would be suitable as a textbook for an undergraduate or elementary graduate course in ordinary differential equations, the authors have designed the text also to be useful for motivated students wishing to learn the material on their own or desiring to supplement an ODE textbook being used in a course they are taking with a text offering a more conceptual approach to the subject.
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.
Numerical Differential Equations
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Author : John Loustau
language : en
Publisher: World Scientific
Release Date : 2016-03-07
Numerical Differential Equations written by John Loustau and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-07 with Mathematics categories.
This text presents numerical differential equations to graduate (doctoral) students. It includes the three standard approaches to numerical PDE, FDM, FEM and CM, and the two most common time stepping techniques, FDM and Runge-Kutta. We present both the numerical technique and the supporting theory. The applied techniques include those that arise in the present literature. The supporting mathematical theory includes the general convergence theory. This material should be readily accessible to students with basic knowledge of mathematical analysis, Lebesgue measure and the basics of Hilbert spaces and Banach spaces. Nevertheless, we have made the book free standing in most respects. Most importantly, the terminology is introduced, explained and developed as needed. The examples presented are taken from multiple vital application areas including finance, aerospace, mathematical biology and fluid mechanics. The text may be used as the basis for several distinct lecture courses or as a reference. For instance, this text will support a general applications course or an FEM course with theory and applications. The presentation of material is empirically-based as more and more is demanded of the reader as we progress through the material. By the end of the text, the level of detail is reminiscent of journal articles. Indeed, it is our intention that this material be used to launch a research career in numerical PDE. Contents:Modeling and Visualization:Some PreliminariesProblems with Closed Form SolutionNumerical Solutions to Steady-State ProblemsPopulation ModelsTransient Problems in One Spatial DimensionTransient Problems in Two Spatial DimensionsMethods and Theory:Finite Difference MethodFinite Element Method, the TechniquesFinite Element Method, the TheoryCollocation Method Readership: Graduate students and researchers. Key Features:There is no text/reference book that covers as broad a list of techniques as completely and as efficientlyWe accomplish this by judiciously selecting preliminary material that is essential
Elementary Lie Group Analysis And Ordinary Differential Equations
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Author : Nailʹ Khaĭrullovich Ibragimov
language : en
Publisher: John Wiley & Sons
Release Date : 1999-05-04
Elementary Lie Group Analysis And Ordinary Differential Equations written by Nailʹ Khaĭrullovich Ibragimov and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-05-04 with Mathematics categories.
Lie group analysis, based on symmetry and invariance principles, is the only systematic method for solving nonlinear differential equations analytically. One of Lie's striking achievements was the discovery that the majority of classical devices for integration of special types of ordinary differential equations could be explained and deduced by his theory. Moreover, this theory provides a universal tool for tackling considerable numbers of differential equations when other means of integration fail. * This is the first modern text on ordinary differential equations where the basic integration methods are derived from Lie group theory * Includes a concise and self contained introduction to differential equations * Easy to follow and comprehensive introduction to Lie group analysis * The methods described in this book have many applications The author provides students and their teachers with a flexible text for undergraduate and postgraduate courses, spanning a variety of topics from the basic theory through to its many applications. The philosophy of Lie groups has become an essential part of the mathematical culture for anyone investigating mathematical models of physical, engineering and natural problems.