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Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations


Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations



von: Xinyuan Wu, Bin Wang

106,99 €

Verlag: Springer
Format: PDF
Veröffentl.: 19.04.2018
ISBN/EAN: 9789811090042
Sprache: englisch

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Beschreibungen

The main theme of this&nbsp;book&nbsp;is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the&nbsp;latest&nbsp;advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods,&nbsp;and&nbsp;symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the&nbsp;context&nbsp;of structure preservation. All the new methods introduced in this book&nbsp;are proven&nbsp;to be highly&nbsp;effective compared with the well-known codes in the scientific literature. This&nbsp;book&nbsp;also addresses&nbsp;challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.<br><p></p>
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</p>
<div>The main theme of this&nbsp;book&nbsp;is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the&nbsp;latest&nbsp;advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods,&nbsp;and&nbsp;symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the&nbsp;context&nbsp;of structure preservation. All the new methods introduced in this book&nbsp;are proven&nbsp;to be highly&nbsp;effective compared with the well-known codes in the scientific literature. This&nbsp;book&nbsp;also addresses&nbsp;challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.<br></div>
<p>Reflects the current state of the art in the area, characterized by mathematical analysis</p><p>Provides insights into questions of practical calculation, and highlights numerical simulations</p><p>Presents modern tools and techniques and introduces competitive new methods</p>

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