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.
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 2012-09-29 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.
Download or read book Decomposition Analysis Method in Linear and Nonlinear Differential Equations written by Kansari Haldar and published by CRC Press. This book was released on 2015-10-22 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Powerful Methodology for Solving All Types of Differential EquationsDecomposition Analysis Method in Linear and Non-Linear Differential Equations explains how the Adomian decomposition method can solve differential equations for the series solutions of fundamental problems in physics, astrophysics, chemistry, biology, medicine, and other scientif
Download or read book Reducible and Irreducible Linear Differential Equations written by Frederic Howell Miller and published by . This book was released on 1932 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
Download or read book Introduction to the Theory of Linear Differential Equations written by Edgar Girard Croker Poole and published by . This book was released on 1936 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Differential Equations written by Daniel Zwillinger and published by CRC Press. This book was released on 2021-12-30 with total page 737 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear Differential Equations in the Complex Domain written by Yasutaka Sibuya and published by American Mathematical Soc.. This book was released on 2008-06-26 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation of a 1976 book originally written in Japanese. The main attention is paid to intrinsic aspects of problems related to linear ordinary differential equations in complex domains. Examples of the problems discussed in the book include the Riemann problem on the Riemann sphere, a characterization of regular singularities, and a classification of meromorphic differential equations. Since the original book was published, many new ideas have developed, such as applications of D-modules, Gevrey asymptotics, cohomological methods, $k$-summability, and studies of differential equations containing parameters. Five appendices, added in the present edition, briefly cover these new ideas. In addition, more than 100 references have been added. This book introduces the reader to the essential facts concerning the structure of solutions of linear differential equations in the complex domain and illuminates the intrinsic meaning of older results by means of more modern ideas. A useful reference for research mathematicians, this book would also be suitable as a textbook in a graduate course or seminar.
Download or read book A Treatise on Linear Differential Equations written by Thomas Craig and published by . This book was released on 1889 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations written by Tarek Mathew and published by Springer Science & Business Media. This book was released on 2008-06-25 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.
Download or read book Linear Ordinary Differential Equations written by Earl A. Coddington and published by Cambridge University Press. This book was released on 1997 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough development of the main topics in linear differential equations with applications, examples, and exercises illustrating each topic.
Download or read book Invariants of Systems of Linear Differential Equations written by Ernest Julius Wilczynski and published by . This book was released on 1901 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Solving Second Order Differential Equations by Decomposition written by Fritz Schwarz and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this article are linear and quasilinear differential equations of second order that may be decomposed into a first-order component with guaranteed solution procedure for obtaining closed-form solutions. These are homogeneous or inhomogeneous linear components, special Riccati components, Bernoulli, Clairaut or d,ÄôAlembert components. Procedures are described how they may be determined and how solutions of the originally given second order equation may be obtained from them. This makes it possible to solve new classes of differential equations and opens up a new area of research. Applying decomposition to linear inhomogeneous equations a simple procedure for determining a special solution follows. It is not based on the method of variation of constants of Lagrange, and consequently does not require the knowledge of a fundamental system. Algorithms based on these results are implemented in the computer algebra system ALLTYPES which is available on the website www.alltypes.de.
Download or read book Algebraic Theory of Differential Equations written by and published by Cambridge University Press. This book was released on with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to the Theory of Linear Differential Equations written by E. G. C. Poole and published by . This book was released on 1956 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ordinary Differential Equations written by Wolfgang Walter and published by Springer. This book was released on 1998-07-01 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on a translation of the 6th edition of Gewöhnliche Differentialgleichungen by Wolfgang Walter, this edition includes additional treatments of important subjects not found in the German text as well as material that is seldom found in textbooks, such as new proofs for basic theorems. This unique feature of the book calls for a closer look at contents and methods with an emphasis on subjects outside the mainstream. Exercises, which range from routine to demanding, are dispersed throughout the text and some include an outline of the solution. Applications from mechanics to mathematical biology are included and solutions of selected exercises are found at the end of the book. It is suitable for mathematics, physics, and computer science graduate students to be used as collateral reading and as a reference source for mathematicians. Readers should have a sound knowledge of infinitesimal calculus and be familiar with basic notions from linear algebra; functional analysis is developed in the text when needed.
