By Xinyuan Wu, Kai Liu, Wei Shi
This e-book describes numerous powerful and effective structure-preserving algorithms for second-order oscillatory differential equations. Such structures come up in lots of branches of technological know-how and engineering, and the examples within the booklet contain platforms from quantum physics, celestial mechanics and electronics. To safely simulate the genuine habit of such structures, a numerical set of rules needs to protect up to attainable their key structural homes: time-reversibility, oscillation, symplecticity, and effort and momentum conservation. The ebook describes novel advances in RKN tools, ERKN equipment, Filon-type asymptotic equipment, AVF equipment, and trigonometric Fourier collocation methods. The accuracy and potency of every of those algorithms are proven through cautious numerical simulations, and their structure-preserving homes are carefully tested by way of theoretical research. The publication additionally provides insights into the sensible implementation of the methods.
This booklet is meant for engineers and scientists investigating oscillatory structures, in addition to for lecturers and scholars who're drawn to structure-preserving algorithms for differential equations.
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