Geometric Integrators for Differential Equations with Highly Oscillatory Solutions (Hardcover, 1st ed. 2021)

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.

General

Imprint:	Springer Verlag, Singapore
Country of origin:	Singapore
Release date:	September 2021
First published:	2021
Authors:	Xinyuan Wu • Bin Wang
Dimensions:	235 x 155mm (L x W)
Format:	Hardcover
Pages:	499
Edition:	1st ed. 2021
ISBN-13:	978-981-16-0146-0
Categories:	Books > Science & Mathematics > Mathematics > Numerical analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis Books > Science & Mathematics > Mathematics > Applied mathematics > Non-linear science Books > Professional & Technical > Mechanical engineering & materials > Materials science > Mechanics of solids > Dynamics & vibration Promotions
LSN:	981-16-0146-1
Barcode:	9789811601460

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