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Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations pp 167–192Cite as

Trigonometric Collocation Methods for Multi-frequency and Multidimensional Oscillatory Systems

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Abstract

This chapter presents a class of trigonometric collocation methods based on Lagrange basis polynomials for solving multi-frequency and multidimensional oscillatory systems \(q^{\prime \prime }(t)+Mq(t)=f\big (q(t)\big )\). The properties of the collocation methods are investigated in detail. It is shown that the convergence condition of these methods is independent of \(\left\| M\right\| \), which is crucial for solving multi-frequency oscillatory systems.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, Jiangsu, China

    Xinyuan Wu

  2. School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, China

    Xinyuan Wu & Bin Wang

Authors
  1. Xinyuan Wu
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  2. Bin Wang
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Correspondence to Xinyuan Wu .

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Wu, X., Wang, B. (2018). Trigonometric Collocation Methods for Multi-frequency and Multidimensional Oscillatory Systems. In: Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations. Springer, Singapore. https://doi.org/10.1007/978-981-10-9004-2_7

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