Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations, Xinyuan Wu; Bin Wang

Автор: Wu
Название: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations
ISBN: 9811090033 ISBN-13(EAN): 9789811090035
Издательство: Springer
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Цена: 102480.00 T
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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: Wu Xinyuan
Название: Structure-Preserving Algorithms for Oscillatory Differential
ISBN: 3642353371 ISBN-13(EAN): 9783642353376
Издательство: Springer
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Цена: 130610.00 T
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Описание: Structure-Preserving Algorithms for Oscillatory Differential Equations describes a large number of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations by using theoretical analysis and numerical validation.

Автор: Alfredo Dea?o, Daan Huybrechs, Arieh Iserles
Название: Computing Highly Oscillatory Integrals
ISBN: 1611975115 ISBN-13(EAN): 9781611975116
Издательство: Mare Nostrum (Eurospan)
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Цена: 70230.00 T
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Описание: Highly oscillatory phenomena range across numerous areas in science and engineering and their computation represents a difficult challenge. A case in point is integrals of rapidly oscillating functions in one or more variables. The quadrature of such integrals has been historically considered very demanding. Research in the past 15 years (in which the authors played a major role) resulted in a range of very effective and affordable algorithms for highly oscillatory quadrature. This is the only monograph bringing together the new body of ideas in this area in its entirety.The starting point is that approximations need to be analyzed using asymptotic methods rather than by more standard polynomial expansions. As often happens in computational mathematics, once a phenomenon is understood from a mathematical standpoint, effective algorithms follow. As reviewed in this monograph, we now have at our disposal a number of very effective quadrature methods for highly oscillatory integrals—Filon-type and Levin-type methods, methods based on steepest descent, and complex-valued Gaussian quadrature. Their understanding calls for a fairly varied mathematical toolbox—from classical numerical analysis, approximation theory, and theory of orthogonal polynomials all the way to asymptotic analysis—yet this understanding is the cornerstone of efficient algorithms.

Автор: Margarita G. Kuzmina, Eduard A. Manykin, Evgeny S.
Название: Oscillatory Neural Networks: In Problems of Parallel Information Processing
ISBN: 3110268353 ISBN-13(EAN): 9783110268355
Издательство: Walter de Gruyter
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Цена: 161100.00 T
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Описание: Understanding of the human brain functioning currently represents a challenging problem. In contrast to usual serial computers and complicated hierarchically organized artificial man-made systems, decentralized, parallel and distributed information processing principles are inherent to the brain. Besides adaptation and learning, which play a crucial role in brain functioning, oscillatory neural activity, synchronization and resonance accompany the brain work. Neural-like oscillatory network models, designed by the authors for image processing, allow to elucidate the capabilities of dynamical, synchronization-based types of image processing, presumably exploited by the brain. The oscillatory network models, studied by means of computer modeling and qualitative analysis, are presented and discussed in the book. Some other problems of parallel distributed information processing are also considered, such as a recall process from network memory for large-scale recurrent associative memory neural networks, performance of oscillatory networks of associative memory, dynamical oscillatory network methods of image processing with synchronization-based performance, optical parallel information processing based on the nonlinear optical phenomenon of photon echo, and modeling random electric fields of quasi-monochromatic polarized light beams using systems of superposed stochastic oscillators. This makes the book highly interesting to researchers dealing with various aspects of parallel information processing.

Автор: Grigory V. Osipov; J?rgen Kurths; Changsong Zhou
Название: Synchronization in Oscillatory Networks
ISBN: 3642090354 ISBN-13(EAN): 9783642090356
Издательство: Springer
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Цена: 95770.00 T
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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: Hairer, E.
Название: Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
ISBN: 3540306633 ISBN-13(EAN): 9783540306634
Издательство: Springer
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Цена: 149060.00 T
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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.

Автор: Tsung-Ming Huang, Ren-Cang Li, Wen-Wei Lin
Название: Structure-Preserving Doubling Algorithms for Nonlinear Matrix Equations
ISBN: 1611975352 ISBN-13(EAN): 9781611975352
Издательство: Mare Nostrum (Eurospan)
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Цена: 53090.00 T
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Описание: Nonlinear matrix equations arise frequently in applied science and engineering. This is the first book to provide a unified treatment of structure-preserving doubling algorithms, which have been recently studied and proven effective for notoriously challenging problems, such as fluid queue theory and vibration analysis for high-speed trains. The authors present recent developments and results for the theory of doubling algorithms for nonlinear matrix equations associated with regular matrix pencils, and highlight the use of these algorithms in achieving robust solutions for notoriously challenging problems that other methods cannot.Structure-Preserving Doubling Algorithms for Nonlinear Matrix Equations is intended for researchers and computational scientists. Graduate students may also find it of interest.

Автор: Stefan Frei, B?rbel Holm, Thomas Richter, Thomas W
Название: Fluid-Structure Interaction: Modeling, Adaptive Discretisations and Solvers
ISBN: 3110495279 ISBN-13(EAN): 9783110495270
Издательство: Walter de Gruyter
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Цена: 148700.00 T
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Описание: This monograph discusses modeling, adaptive discretisation techniques and the numerical solution of fluid structure interaction. An emphasis in part I lies on innovative discretisation and advanced interface resolution techniques. The second part covers the efficient and robust numerical solution of fluid-structure interaction. In part III, recent advances in the application fields vascular flows, binary-fluid-solid interaction, and coupling to fractures in the solid part are presented. Moreover each chapter provides a comprehensive overview in the respective topics including many references to concurring state-of-the art work. ContentsPart I: Modeling and discretizationOn the implementation and benchmarking of an extended ALE method for FSI problemsThe locally adapted parametric finite element method for interface problems on triangular meshesAn accurate Eulerian approach for fluid-structure interactions Part II: SolversNumerical methods for unsteady thermal fluid structure interactionRecent development of robust monolithic fluid-structure interaction solversA monolithic FSI solver applied to the FSI 1,2,3 benchmarks Part III: ApplicationsFluid-structure interaction for vascular flows: From supercomputers to laptopsBinary-fluid–solid interaction based on the Navier–Stokes–Cahn–Hilliard EquationsCoupling fluid-structure interaction with phase-field fracture: Algorithmic details

Автор: Juan Luis Garc?a Guirao; Jos? Alberto Murillo Hern
Название: Recent Advances in Differential Equations and Applications
ISBN: 303000340X ISBN-13(EAN): 9783030003401
Издательство: Springer
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Цена: 93160.00 T
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Описание: This work gathers a selection of outstanding papers presented at the 25th Conference on Differential Equations and Applications / 15th Conference on Applied Mathematics, held in Cartagena, Spain, in June 2017. It supports further research into both ordinary and partial differential equations, numerical analysis, dynamical systems, control and optimization, trending topics in numerical linear algebra, and the applications of mathematics to industry. The book includes 14 peer-reviewed contributions and mainly addresses researchers interested in the applications of mathematics, especially in science and engineering. It will also greatly benefit PhD students in applied mathematics, engineering and physics.

Автор: Ferenc Hartung; Mih?ly Pituk
Название: Recent Advances in Delay Differential and Difference Equations
ISBN: 3319378678 ISBN-13(EAN): 9783319378671
Издательство: Springer
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Цена: 93160.00 T
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Описание: Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering and control theory.

Автор: Robinson
Название: Recent Progress in the Theory of the Euler and Navier–Stokes Equations
ISBN: 1107554977 ISBN-13(EAN): 9781107554979
Издательство: Cambridge Academ
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Цена: 61240.00 T
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Описание: This survey volume provides an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. It serves both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

Автор: Vicentiu D. Radulescu, Adelia Sequeira, Vsevolod A. Solonnikov
Название: Recent Advances in Partial Differential Equations and Applications
ISBN: 1470415216 ISBN-13(EAN): 9781470415211
Издательство: Mare Nostrum (Eurospan)
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Цена: 108110.00 T
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Описание: Contains the proceedings of the International Conference on Recent Advances in PDEs and Applications, held in February 2014. The conference brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants.