Geometric Integrators for Differential Equations with Highly Oscillatory Solutions

Xinyuan Wu, Bin Wang

PDF
ca. 90,94 €
Amazon iTunes Thalia.de Hugendubel Bücher.de ebook.de kobo Osiander Google Books Barnes&Noble bol.com Legimi yourbook.shop Kulturkaufhaus ebooks-center.de
* Affiliatelinks/Werbelinks
Hinweis: Affiliatelinks/Werbelinks
Links auf reinlesen.de sind sogenannte Affiliate-Links. Wenn du auf so einen Affiliate-Link klickst und über diesen Link einkaufst, bekommt reinlesen.de von dem betreffenden Online-Shop oder Anbieter eine Provision. Für dich verändert sich der Preis nicht.

Springer Singapore img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Analysis

Beschreibung

The idea of structure-preserving algorithms appeared in the 1980's. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or the existence of conservation laws or some other qualitative feature of the dynamics. Another area that has kept growing in importance within Geometric Numerical Integration is the study of highly-oscillatory problems: problems where the solutions are periodic or quasiperiodic and have to be studied in time intervals that include an extremely large number of periods. As is known, these equations cannot be solved efficiently using conventional methods. A further study of novel geometric integrators has become increasingly important in recent years. The objective of this monograph is to explore further geometric integrators for highly oscillatory problems that can be formulated as systems of ordinary and partial differential equations.


Facing challenging scientific computational problems, this book presents some new perspectives of the subject matter based on theoretical derivations and mathematical analysis, and provides high-performance numerical simulations. In order to show the long-time numerical behaviour of the simulation, all the integrators presented in this monograph have been tested and verified on highly oscillatory systems from a wide range of applications in the field of science and engineering. They are more efficient than existing schemes in the literature for differential equations that have highly oscillatory solutions. 

This book is useful to researchers, teachers, students and engineers who are interested in Geometric Integrators and their long-time behaviour analysis for differential equations with highly oscillatory solutions. 

Weitere Titel von diesem Autor
Weitere Titel in dieser Kategorie

Kundenbewertungen

Schlagwörter

Geometric algorithms for conservative or dissipative systems, Oscillation-preserving integrators, Symplectic algorithms, Energy-preserving schemes, Geometric numerical integration, Long-time behaviour of numerical integrators