Loewy Decomposition of Linear Differential Equations PDF Download

Author: Fritz Schwarz
Publisher: Springer Science & Business Media
ISBN: 3709112869
Category : Computers
Languages : en
Pages : 238

View

Book Description
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: Fritz Schwarz
Publisher: CRC Press
ISBN: 1584888903
Category : Mathematics
Languages : en
Pages : 446

View

Book Description
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: Daniel Zwillinger
Publisher: CRC Press
ISBN: 100046816X
Category : Mathematics
Languages : en
Pages : 737

View

Book Description
Through the previous three editions, Handbook of Differential Equations has proven an invaluable reference for anyone working within the field of mathematics, including academics, students, scientists, and professional engineers. The book is a compilation of methods for solving and approximating differential equations. These include the most widely applicable methods for solving and approximating differential equations, as well as numerous methods. Topics include methods for ordinary differential equations, partial differential equations, stochastic differential equations, and systems of such equations. Included for nearly every method are: The types of equations to which the method is applicable The idea behind the method The procedure for carrying out the method At least one simple example of the method Any cautions that should be exercised Notes for more advanced users The fourth edition includes corrections, many supplied by readers, as well as many new methods and techniques. These new and corrected entries make necessary improvements in this edition.

Author: Bruno Carpentieri
Publisher: BoD – Books on Demand
ISBN: 1839686561
Category : Mathematics
Languages : en
Pages : 374

View

Book Description
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:
Publisher: Cambridge University Press
ISBN:
Category :
Languages : en
Pages : 248

View

Book Description

Author: Vladimir P. Gerdt
Publisher: Springer
ISBN: 3319240218
Category : Computers
Languages : en
Pages : 508

View

Book Description
This book constitutes the proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing, CASC 2015, held in Aachen, Germany, in September 2015. The 35 full papers presented in this volume were carefully reviewed and selected from 42 submissions. They deal with the ongoing progress both in theoretical computer algebra and its expanding applications. New and closer interactions are fostered by combining the area of computer algebra methods and systems and the application of the tools of computer algebra for the solution of problems in scientific computing.

Author: Johannes Blümlein
Publisher: Springer Nature
ISBN: 3030802191
Category : Science
Languages : en
Pages : 551

View

Book Description
This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews. The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.

Author: Ilias Kotsireas
Publisher: World Scientific
ISBN: 9812702008
Category : Computers
Languages : en
Pages : 220

View

Book Description
Written by world-renowned experts, the book is a collection of tutorial presentations and research papers catering to the latest advances in symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. The papers were presented at a workshop celebrating the 60th birthday of Sergei Abramov (Russia), whose highly influential contributions to symbolic methods are adopted in many leading computer algebra systems.

Author: Ilias S Kotsireas
Publisher: World Scientific
ISBN: 9814476692
Category : Computers
Languages : en
Pages : 220

View

Book Description
Written by world-renowned experts, the book is a collection of tutorial presentations and research papers catering to the latest advances in symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. The papers were presented at a workshop celebrating the 60th birthday of Sergei Abramov (Russia), whose highly influential contributions to symbolic methods are adopted in many leading computer algebra systems.

Author: Jacques Carette
Publisher: Springer Science & Business Media
ISBN: 3642026141
Category : Computers
Languages : en
Pages : 510

View

Book Description
As computers and communications technology advance, greater opportunities arise for intelligent mathematical computation. While computer algebra, au- mated deduction and mathematical publishing each have long and successful histories, we are now seeing increasing opportunities for synergy among them. The Conferences on Intelligent Computer Mathematics (cicm 2009) is a c- lection of co-located meetings, allowing researchers and practitioners active in these related areas to share recent results and identify the next challenges. The speci?c areas of the cicm conferences and workshops are described below, but the unifying theme is the computerized handling of mathematical knowledge. The successful formalization of much of mathematics, as well as a better - derstanding of its internal structure, makes mathematical knowledge in many waysmore tractable than generalknowledge,as traditionally treatedin arti?cial intelligence. Similarly, we can also expect the problem of e?ectively using ma- ematical knowledge in automated ways to be much more tractable. This is the goal of the work in the cicm conferences and workshops. In the long view, so- ing the problems addressed by cicm is an important milestone in formulating the next generation of mathematical software.