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