Trigonometric Collocation Methods for Multi-frequency and Multidimensional Oscillatory Systems

Xinyuan Wu () and Bin Wang
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Xinyuan Wu: Nanjing University, Department of Mathematics
Bin Wang: Qufu Normal University, School of Mathematical Sciences

Chapter Chapter 7 in Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations, 2018, pp 167-192 from Springer

Abstract: Abstract This chapter presents a class ofTrigonometric collocation method trigonometric collocation methods based on Lagrange basis polynomials for solving multi-frequencyMulti-frequency and multidimensional oscillatory systems 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.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-10-9004-2_7

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DOI: 10.1007/978-981-10-9004-2_7

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