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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