Structure-Preserving Algorithms for Oscillatory Differential Equations II

• Κύριοι συγγραφείς: Wu, Xinyuan (Συγγραφέας), Liu, Kai (Συγγραφέας), Shi, Wei (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015.
• Έκδοση: 1st ed. 2015.
• Θέματα: Engineering.; Computer mathematics.; Physics.; Applied mathematics.; Engineering mathematics.; Appl.Mathematics/Computational Methods of Engineering.; Theoretical, Mathematical and Computational Physics.; Computational Science and Engineering.

This book describes a variety of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations. Such systems arise in many branches of science and engineering, and the examples in the book include systems from quantum physics, celestial mechanics...

Πίνακας περιεχομένων:

• Matrix-variation-of-constants formula
• Improved St ¨ormer-Verlet formulae with applications
• Improved Filon-type asymptotic methods for highly oscillatory differential equations
• Efficient energy-preserving integrators for multi-frequency oscillatory Hamiltonian systems
• An extended discrete gradient formula for multi-frequency oscillatory Hamiltonian systems
• Trigonometric Fourier collocation methods for multi-frequency oscillatory systems
• Error bounds for explicit ERKN integrators for multi-frequency oscillatory systems
• Error analysis of explicit TSERKN methods for highly oscillatory systems
• Highly accurate explicit symplectic ERKN methods for multi-frequency oscillatory Hamiltonian systems
• Multidimensional ARKN methods for general multi-frequency oscillatory second-order IVPs
• A simplified Nystr¨om-tree theory for ERKN integrators solving oscillatory systems
• An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations.