Algorithmic Lie Theory For Solving Ordinary Differential Equations
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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
Loewy Decomposition Of Linear Differential Equations
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Author : Fritz Schwarz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-28
Loewy Decomposition Of Linear Differential Equations written by Fritz Schwarz 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 2012-09-28 with Computers categories.
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.
Recent Developments In The Solution Of Nonlinear Differential Equations
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Author : Bruno Carpentieri
language : en
Publisher: BoD – Books on Demand
Release Date : 2021-09-08
Recent Developments In The Solution Of Nonlinear Differential Equations written by Bruno Carpentieri and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-08 with Mathematics categories.
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.
An Introduction To Linear Ordinary Differential Equations Using The Impulsive Response Method And Factorization
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Author : Roberto Camporesi
language : en
Publisher: Springer
Release Date : 2016-12-08
An Introduction To Linear Ordinary Differential Equations Using The Impulsive Response Method And Factorization written by Roberto Camporesi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-08 with Mathematics categories.
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.
Symbolic And Numerical Scientific Computation
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Author : Franz Winkler
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-30
Symbolic And Numerical Scientific Computation written by Franz Winkler 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 2003-06-30 with Computers categories.
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.
Groups Invariants Integrals And Mathematical Physics
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Author : Maria Ulan
language : en
Publisher: Springer Nature
Release Date : 2023-05-31
Groups Invariants Integrals And Mathematical Physics written by Maria Ulan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-31 with Science categories.
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.
Algorithms Using Lie Tranformation Groups To Solve First Order Ordinary Differential Equations Algebraically
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Author : Bruce Walter Char
language : en
Publisher:
Release Date : 1980
Algorithms Using Lie Tranformation Groups To Solve First Order Ordinary Differential Equations Algebraically written by Bruce Walter Char and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.
Differential Equations With Maxima
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Author : Drumi D. Bainov
language : en
Publisher: CRC Press
Release Date : 2011-04-28
Differential Equations With Maxima written by Drumi D. Bainov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-28 with Mathematics categories.
Differential equations with "maxima"-differential equations that contain the maximum of the unknown function over a previous interval-adequately model real-world processes whose present state significantly depends on the maximum value of the state on a past time interval. More and more, these equations model and regulate the behavior of various tec
Geomathematically Oriented Potential Theory
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Author : Willi Freeden
language : en
Publisher: CRC Press
Release Date : 2012-10-30
Geomathematically Oriented Potential Theory written by Willi Freeden and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-30 with Mathematics categories.
As the Earth`s surface deviates from its spherical shape by less than 0.4 percent of its radius and today's satellite missions collect their gravitational and magnetic data on nearly spherical orbits, sphere-oriented mathematical methods and tools play important roles in studying the Earth's gravitational and magnetic field. Geomathematically Orien
The Separable Galois Theory Of Commutative Rings
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Author : Andy R. Magid
language : en
Publisher: CRC Press
Release Date : 2014-07-14
The Separable Galois Theory Of Commutative Rings written by Andy R. Magid and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
The Separable Galois Theory of Commutative Rings, Second Edition provides a complete and self-contained account of the Galois theory of commutative rings from the viewpoint of categorical classification theorems and using solely the techniques of commutative algebra. Along with updating nearly every result and explanation, this edition contains a n