Описание: The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g., in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented.
Автор: Jan Awrejcewicz Название: Ordinary Differential Equations and Mechanical Systems ISBN: 331935289X ISBN-13(EAN): 9783319352893 Издательство: Springer Рейтинг: Цена: 15372.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 1. Introduction.- 2. First order ODEs.- 3. Second order ODEs.- 4. Linear ODEs.- 5. Higher-order ODEs polynomial form.- 6. Systems.- 7. Theory and criteria of similarity.- 8. Model and modeling.- 9. Phase plane and phase space.- 10. Stability.- 11. Modeling via perturbation methods.- 12. Continualization and discretization.- 13. Bifurcations.- 14. Optimization of systems.- 15. Chaos and synchronization.
Описание: 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.
Описание: Part of the "CISM International Centre for Mechanical Sciences", this work covers a wide range of research topics in the field of dynamical systems and applications of non-linear analysis to ordinary and partial differential equations.
Автор: Jan Awrejcewicz Название: Ordinary Differential Equations and Mechanical Systems ISBN: 3319076582 ISBN-13(EAN): 9783319076584 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Ordinary Differential Equations and Mechanical Systems
Автор: Chicone Название: Ordinary Differential Equations with Applications ISBN: 0387307699 ISBN-13(EAN): 9780387307695 Издательство: Springer Рейтинг: Цена: 12577.00 р. Наличие на складе: Поставка под заказ.
Описание: A text for a graduate level course in the theory of ordinary differential equations. It contains theory and applications. It links ordinary differential equations with advanced mathematical topics such as differential geometry, Lie group theory, analysis in infinite-dimensional spaces and abstract algebra.
Автор: Van der Put Marius , Singer Michael F. Название: Galois Theory of Linear Differential Equations ISBN: 3540442286 ISBN-13(EAN): 9783540442288 Издательство: Springer Рейтинг: Цена: 13969.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Linear differential equations form the central topic of this volume, Galois theory being the unifying theme.A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, the inverse problem and linear differential equations in positive characteristic. The appendices aim to help the reader with concepts used, from algebraic geometry, linear algebraic groups, sheaves, and tannakian categories that are used. This volume will become a standard reference for all mathematicians in this area of mathematics, including graduate students.
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