Structure-Preserving Algorithms for Oscillatory Differential, Wu Xinyuan
Автор: Livija Cveticanin Название: Strong Nonlinear Oscillators ISBN: 3319588257 ISBN-13(EAN): 9783319588254 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book outlines an analytical solution procedure of the pure nonlinear oscillator system, offering a solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameter. Includes exercises.
Автор: Qingjie Cao; Alain L?ger Название: A Smooth and Discontinuous Oscillator ISBN: 3662530929 ISBN-13(EAN): 9783662530924 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Background: Nonlinear Systems.- An Smooth and Discontinuous (SD) Oscillator.- Bifurcation Behaviour.- Periodic Motions of the Perturbed SD Oscillator.- The Exact Solutions.- Chaotic Motions of the SD Oscillator.- Experimental Investigation of the SD Oscillator.- Applications in Structural Dynamics.- Applications in Engineering Isolation.- Challenges and the Open Problems.
Описание: This book describes effective and efficient structure-preserving algorithms for second-order oscillatory differential equations by using theoretical analysis and numerical validation. Includes advances in ARKN, ERKN, Falkner-type and energy-preserving methods.
Описание: Functionally fitted continuous finite element methods for oscillatory Hamiltonian system.- Exponential average-vector-field integrator for conservative or dissipative systems.- Exponential Fourier collocation methods for first-order differential Equations.- Symplectic exponential Runge-Kutta methods for solving nonlinear Hamiltonian systems.- High-order symplectic and symmetric composition integrators for multi-frequency oscillatory Hamiltonian systems.- The construction of arbitrary order ERKN integrators via group theory.- Trigonometric collocation methods for multi-frequency and multidimensional oscillatory systems.- A compact tri-colored tree theory for general ERKN methods.- An integral formula adapted to different boundary conditions for arbitrarily high-dimensional nonlinear Klein-Gordon equations.- An energy-preserving and symmetric scheme for nonlinear Hamiltonian wave equations.- Arbitrarily high-order time-stepping schemes for nonlinear Klein-Gordon equations.- An essential extension of the finite-energy condition for ERKN integrators solving nonlinear wave equations.- Index
Автор: Grigory V. Osipov; J?rgen Kurths; Changsong Zhou Название: Synchronization in Oscillatory Networks ISBN: 3642090354 ISBN-13(EAN): 9783642090356 Издательство: Springer Рейтинг: Цена: 14365.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This work systematically investigates a large number of oscillatory network configurations that are able to describe many real systems such as electric power grids, lasers or even the heart muscle, to name but a few.
Автор: Gitterman Moshe Название: Oscillator And Pendulum With A Random Mass ISBN: 9814630748 ISBN-13(EAN): 9789814630740 Издательство: World Scientific Publishing Рейтинг: Цена: 10771.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Stochastic descriptions of a harmonic oscillator can be obtained by adding additive noise, or/and three types of multiplicative noise: random frequency, random damping and random mass. The first three types of noise were intensively studied in many published articles. In this book the fourth case, that of random mass, is considered in the context of the harmonic oscillator and its immediate nonlinear generalization -- the pendulum. To our knowledge it is the first book fully dedicated to this problem.
Two interrelated methods, the Langevin equation and the Fokker-Planck equations, as well as the Lyapunov stability method are used for the mathematical analysis. After a short introduction, the two main parts of the book describe the different properties of the random harmonic oscillator and the random pendulum with random masses. As an example, the stochastic resonance is studied, where the noise plays an unusual role, increasing the applied weak periodic signal, and also the vibration resonance in dynamic systems, where the role of noise is played by the second high-frequency periodic signal.
First and second averaged moments have been calculated for a system with different types of additive and multiplicative noises, which define the stability of a system. The calculations have been extended to two multiplicative noises and to quadratic noise. This book is useful for students and scientists working in different fields of statistical physics.
This book consists of the articles published in the special issues of this Symmetry journal based on two-by-two matrices and harmonic oscillators. The book also contains additional articles published by the guest editor in this Symmetry journal. They are of course based on harmonic oscillators and/or two-by-two matrices. The subject of symmetry is based on exactly soluble problems in physics, and the physical theory is not soluble unless it is based on oscillators and/or two-by-two matrices. The authors of those two special issues were aware of this environment when they submitted their articles. This book could therefore serve as an example to illustrate this important aspect of symmetry problems in physics.
Описание: This book grew out of a series of lectures given at the Mathematics Department of Kyushu University in the Fall 2006, within the support of the 21st Century COE Program (2003-2007) "Development of Dynamical Mathematics with High Fu- tionality" (Program Leader: prof. Mitsuhiro Nakao). It was initially published as the Kyushu University COE Lecture Note n- ber 8 (COE Lecture Note, 8. Kyushu University, The 21st Century COE Program "DMHF," Fukuoka, 2008. vi+234 pp.), and in the present form is an extended v- sion of it (in particular, I have added a section dedicated to the Maslov index). The book is intended as a rapid (though not so straightforward) pseudodiff- ential introduction to the spectral theory of certain systems, mainly of the form a +a where the entries of a are homogeneous polynomials of degree 2 in the 2 0 2 n n (x, ?)-variables, (x, ?)? R R, and a is a constant matrix, the so-called non- 0 commutative harmonic oscillators, with particular emphasis on a class of systems introduced by M. Wakayama and myself about ten years ago. The class of n- commutative harmonic oscillators is very rich, and many problems are still open, and worth of being pursued.
Описание: This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. The long-time behavior of the numerical solutions is studied using a backward error analysis combined with KAM theory.
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