An efficient method to approximate eigenfunctions and high-index eigenvalues of regular Sturm-Liouville problems

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• 作者：M. Dehghan ; ^{dehghan@iausari.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; ^{m-dehghan@tabrizu.ac.ir" class="auth_mail" title="E-mail the corresponding author} ; ^{m_dehghan83@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Sturm&ndash ; Liouville equation ; Eigenvalue ; Eigenfunction ; Highly oscillating integral ; Asymptotic behavior
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：10 April 2016
• 年：2016
• 卷：279
• 期：Complete
• 页码：249-257
• 全文大小：459 K

文摘

The computation of the eigenvalues of a Sturm–Liouville problem is a difficult task, when high-index eigenvalues are computed. In most previous methods, it can be seen that the uncertainty of the results increases as the estimated eigenvalues grow larger. This paper is to present some new methods in which, not only the error of calculating the higher eigenvalues does not grow, but it also vanishes as eigenvalues tend to infinity. Moreover, the proposed method gives good estimates of eigenfunctions corresponding to high eigenvalues.