A SPECTRAL COLLOCATION METHOD FOR EIGENVALUE PROBLEMS OF COMPACT INTEGRAL OPERATORS

作者：Huang Can^*; Guo Hailong; Zhang Zhimin

来源：Journal of Integral Equations and Applications, 2013, 25(1): 79-101.

DOI：10.1216/JIE-2013-25-1-79

• Eigenvalue problem
• spectral collocation method
• weakly singular kernel
• integral operator
• super-geometric convergence

We propose and analyze a new spectral collocation method to solve eigenvalue problems of compact integral operators, particularly, piecewise smooth operator kernels and weakly singular operator kernels of the form 1/vertical bar t - s vertical bar(mu), 0 %26lt; mu %26lt; 1. We prove that the convergence rate of eigenvalue approximation depends upon the smoothness of the corresponding eigenfunctions for piecewise smooth kernels. On the other hand, we can numerically obtain a higher rate of convergence for the above weakly singular kernel for some mu%26apos;s even if the eigenfunction is not smooth. Numerical experiments confirm our theoretical results.

• 出版日期2013
• 单位北京计算科学研究中心