Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations

详细信息    查看全文

• 作者：Bin Wang^a ; ^{wangbinmaths@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Xinyuan Wu^b ; ^{xywu@nju.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Fanwei Meng^a ; ^{fwmeng@mail.qfnu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65L05 ; 65L06 ; 34C15 ; 34E05
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：313
• 期：Complete
• 页码：185-201
• 全文大小：698 K

文摘

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^″(t)+Mq(t)=f(q(t))$q^{″}\left(t\right)+Mq\left(t\right)=f\left(q\left(t\right)\right)$. The properties of the obtained methods are investigated. It is shown that the convergent condition of these methods is independent of ‖M‖$\Vert M\Vert$, 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.