Hybrid collocation methods for eigenvalue problem of a compact integral operator with weakly singular kernel. (English) Zbl 1427.65424
Summary: In this paper, we consider the hybrid collocation methods to solve the eigenvalue problem of a compact integral operator with weakly singular kernels of algebraic and logarithmic type. We obtain the global convergence rates for eigenvalues, the gap between the spectral subspaces and iterated eigenvectors. The numerical examples are presented to verify the theoretical estimates and also shown that this method is computationally useful in comparison to other methods.
MSC:
| 65R20 | Numerical methods for integral equations |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 45B05 | Fredholm integral equations |
| 45C05 | Eigenvalue problems for integral equations |
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