In the present work, a kind of trigonometric collocation methods based on Lagrange basis polynomials is developed for effectively solving multi-frequency oscillatory second-order differential equations $q^{ \prime\prime}(t)+Mq(t)=f\big(q(t)\big)$. The properties of the obtained methods are investigated. It is shown that the convergent condition of these methods is independent of $\norm{ M}$, which is very crucial for solving oscillatory systems. A fourth-order scheme of the methods is presented. Numerical experiments are implemented to show the remarkable efficiency of the methods proposed in this paper.
Categories: math.NA