A Spectral Collocation Method for Eigenvalue Problems of Compact Integral Operators
نویسندگان
چکیده
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 |t−s|μ , 0 < μ < 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 μ’s even if the eigenfunction is not smooth. Numerical experiments confirm our theoretical results.
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