The spectrum of the Gegenbauer Collocation approximation for the second derivative operator

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• 作者：Marios Charalambides ^{bus.chm@fit.ac.cy" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Collocation ; Gegenbauer ; Spectrum ; Stable polynomials ; Spectral methods
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：433
• 期：2
• 页码：1502-1512
• 全文大小：320 K

文摘

It is proved that the eigenvalues of the Gegenbauer Collocation method for the second derivative operator with Dirichlet boundary conditions are real, negative and distinct for a range of the Gegenbauer parameter. This range includes the Chebyshev Collocation approximation. The result is also extended to Neumann and Robin boundary conditions.