Author: Fritz Schwarz
Publisher: Springer Science & Business Media
ISBN: 3709112869
Category : Computers
Languages : en
Pages : 238
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.
Loewy Decomposition of Linear Differential Equations
Author: Fritz Schwarz
Publisher: Springer Science & Business Media
ISBN: 3709112869
Category : Computers
Languages : en
Pages : 238
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.
Publisher: Springer Science & Business Media
ISBN: 3709112869
Category : Computers
Languages : en
Pages : 238
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.
Loewy Decomposition of Linear Differential Equations
Author: Fritz Schwarz
Publisher: Springer Science & Business Media
ISBN: 3709112850
Category : Computers
Languages : en
Pages : 238
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.
Publisher: Springer Science & Business Media
ISBN: 3709112850
Category : Computers
Languages : en
Pages : 238
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.
Decomposition Analysis Method in Linear and Nonlinear Differential Equations
Author: Kansari Haldar
Publisher: CRC Press
ISBN: 1498716342
Category : Mathematics
Languages : en
Pages : 281
Book Description
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
Publisher: CRC Press
ISBN: 1498716342
Category : Mathematics
Languages : en
Pages : 281
Book Description
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
Reducible and Irreducible Linear Differential Equations
Author: Frederic Howell Miller
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 24
Book Description
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 24
Book Description
Algorithmic Lie Theory for Solving Ordinary Differential Equations
Author: Fritz Schwarz
Publisher: CRC Press
ISBN: 9781584888901
Category : Mathematics
Languages : en
Pages : 448
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
Publisher: CRC Press
ISBN: 9781584888901
Category : Mathematics
Languages : en
Pages : 448
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
Introduction to the Theory of Linear Differential Equations
Author: Edgar Girard Croker Poole
Publisher:
ISBN:
Category : Calculus
Languages : en
Pages : 212
Book Description
Publisher:
ISBN:
Category : Calculus
Languages : en
Pages : 212
Book Description
Handbook of Differential Equations
Author: Daniel Zwillinger
Publisher: CRC Press
ISBN: 100046816X
Category : Mathematics
Languages : en
Pages : 737
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.
Publisher: CRC Press
ISBN: 100046816X
Category : Mathematics
Languages : en
Pages : 737
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.
Linear Differential Equations in the Complex Domain
Author: Yasutaka Sibuya
Publisher: American Mathematical Soc.
ISBN: 0821846760
Category : Mathematics
Languages : en
Pages : 286
Book Description
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.
Publisher: American Mathematical Soc.
ISBN: 0821846760
Category : Mathematics
Languages : en
Pages : 286
Book Description
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.
A Treatise on Linear Differential Equations
Author: Thomas Craig
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 538
Book Description
Publisher:
ISBN:
Category : Differential equations, Linear
Languages : en
Pages : 538
Book Description
Recent Developments in the Solution of Nonlinear Differential Equations
Author: Bruno Carpentieri
Publisher: BoD – Books on Demand
ISBN: 1839686561
Category : Mathematics
Languages : en
Pages : 374
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.
Publisher: BoD – Books on Demand
ISBN: 1839686561
Category : Mathematics
Languages : en
Pages : 374
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.