Algorithmic Lie Theory For Solving Ordinary Differential Equations

Author : Fritz Schwarz
Publisher : CRC Press
ISBN 13 : 9781584888901
Total Pages : 448 pages
Book Rating : 4.03/5 ( download)

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Download or read book Algorithmic Lie Theory for Solving Ordinary Differential Equations written by Fritz Schwarz and published by CRC Press. This book was released on 2007-10-02 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Fritz Schwarz
Publisher : Springer Science & Business Media
ISBN 13 : 3709112869
Total Pages : 238 pages
Book Rating : 4.61/5 ( download)

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Download or read book Loewy Decomposition of Linear Differential Equations written by Fritz Schwarz and published by Springer Science & Business Media. This book was released on 2012-09-28 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a single function in two independent variables of order two or three are comprehensively discussed. A complete list of possible solution types is given. Various ad hoc results available in the literature are obtained algorithmically. The border of decidability for generating a Loewy decomposition are explicitly stated. The methods applied may be generalized in an obvious way to equations of higher order, in more variables or systems of such equations.

Author : Bruno Carpentieri
Publisher : BoD – Books on Demand
ISBN 13 : 1839686561
Total Pages : 374 pages
Book Rating : 4.66/5 ( download)

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Download or read book Recent Developments in the Solution of Nonlinear Differential Equations written by Bruno Carpentieri and published by BoD – Books on Demand. This book was released on 2021-09-08 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear differential equations are ubiquitous in computational science and engineering modeling, fluid dynamics, finance, and quantum mechanics, among other areas. Nowadays, solving challenging problems in an industrial setting requires a continuous interplay between the theory of such systems and the development and use of sophisticated computational methods that can guide and support the theoretical findings via practical computer simulations. Owing to the impressive development in computer technology and the introduction of fast numerical methods with reduced algorithmic and memory complexity, rigorous solutions in many applications have become possible. This book collects research papers from leading world experts in the field, highlighting ongoing trends, progress, and open problems in this critically important area of mathematics.

Author : Jane Cronin
Publisher : CRC Press
ISBN 13 : 1420014935
Total Pages : 408 pages
Book Rating : 4.38/5 ( download)

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Download or read book Ordinary Differential Equations written by Jane Cronin and published by CRC Press. This book was released on 2007-12-14 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for a rigorous first course in ordinary differential equations, Ordinary Differential Equations: Introduction and Qualitative Theory, Third Edition includes basic material such as the existence and properties of solutions, linear equations, autonomous equations, and stability as well as more advanced topics in periodic solutions of

Author : Roberto Camporesi
Publisher : Springer
ISBN 13 : 3319496670
Total Pages : 120 pages
Book Rating : 4.72/5 ( download)

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Download or read book An Introduction to Linear Ordinary Differential Equations Using the Impulsive Response Method and Factorization written by Roberto Camporesi and published by Springer. This book was released on 2016-12-08 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana’s result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients.

Author : Bruce Walter Char
Publisher :
ISBN 13 :
Total Pages : 352 pages
Book Rating : 4.39/5 ( download)

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Download or read book Algorithms Using Lie Tranformation Groups to Solve First Order Ordinary Differential Equations Algebraically written by Bruce Walter Char and published by . This book was released on 1980 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Abraham Cohen
Publisher : Forgotten Books
ISBN 13 : 9781331128397
Total Pages : 260 pages
Book Rating : 4.90/5 ( download)

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Download or read book An Introduction to the Lie Theory of One-Parameter Groups written by Abraham Cohen and published by Forgotten Books. This book was released on 2015-06-24 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from An Introduction to the Lie Theory of One-Parameter Groups: With Applications to the Solution of Differential Equations The object of this book is to present in an elementary manner, in English, an introduction to Lie's theory of one-parameter groups, with special reference to its application to the solution of differential equations invariant under such groups. The treatment is sufficiently elementary to be appreciated, under proper supervision, by undergraduates in their senior year as well as by graduates during their first year of study. While a knowledge of the elementary theory of differential equations is not absolutely essential for understanding the subject matter of this book, frequent references being made to places where necessary information can be obtained, it would seem preferable to approach for the first time the problem of classifying and solving differential equations by direct, even if miscellaneous, methods to doing so by the elegant general methods of Lie; and this book is intended primarily for those who have some acquaintance with the elementary theory. To such persons it should prove of great interest and undoubted practical value. An attempt has been made throughout the work to emphasize the role played by the Lie theory in unifying the elementary theory of differential equations, by bringing under a relatively small number of heads the various known classes of differential equations invariant under continuous groups, and the methods for their solution. Special attention may be called to the lists of invariant differential equations and applications in §§ 19, 28, 30; while the two tables in the appendix include most of the ordinary differential equations likely to be met. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Abraham Cohen
Publisher :
ISBN 13 :
Total Pages : 264 pages
Book Rating : 4.11/5 ( download)

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Download or read book An Introduction to the Lie Theory of One-parameter Groups written by Abraham Cohen and published by . This book was released on 1931 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Maria Ulan
Publisher : Springer Nature
ISBN 13 : 3031256662
Total Pages : 263 pages
Book Rating : 4.60/5 ( download)

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Download or read book Groups, Invariants, Integrals, and Mathematical Physics written by Maria Ulan and published by Springer Nature. This book was released on 2023-05-31 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include: The multisymplectic and variational nature of Monge-Ampère equations in dimension four Integrability of fifth-order equations admitting a Lie symmetry algebra Applications of the van Kampen theorem for groupoids to computation of homotopy types of striped surfaces A geometric framework to compare classical systems of PDEs in the category of smooth manifolds Groups, Invariants, Integrals, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and category theory is assumed.

Author : Franz Winkler
Publisher : Springer Science & Business Media
ISBN 13 : 3540405542
Total Pages : 399 pages
Book Rating : 4.42/5 ( download)

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Download or read book Symbolic and Numerical Scientific Computation written by Franz Winkler and published by Springer Science & Business Media. This book was released on 2003-06-30 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-proceedings of the Second International Conference on Symbolic and Numerical Scientific Computation, SNSC 2001, held in Hagenberg, Austria, in September 2001. The 19 revised full papers presented were carefully selected during two rounds of reviewing and improvement. The papers are organized in topical sections on symbolics and numerics of differential equations, symbolics and numerics in algebra and geometry, and applications in physics and engineering.