Sinc-collocation methods with consistent collocation points for Fredholm integral equations of the second kind
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911045941985280 |
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| author | Okayama, Tomoaki |
| author_facet | Okayama, Tomoaki |
| contents | Sinc-collocation methods are known to be efficient for Fredholm integral equations of the second kind, even if functions in the equations have endpoint singularity. However, existing methods have the disadvantage of inconsistent collocation points. This inconsistency complicates the implementation of such methods, particularly for large-scale problems. To overcome this drawback, this study proposes another Sinc-collocation methods with consistent collocation points. The results of a theoretical error analysis show that the proposed methods have the same convergence property as existing methods. Numerical experiments suggest the superiority of the proposed methods in terms of implementation and computational cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_12692 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Sinc-collocation methods with consistent collocation points for Fredholm integral equations of the second kind Okayama, Tomoaki Numerical Analysis 65R20 Sinc-collocation methods are known to be efficient for Fredholm integral equations of the second kind, even if functions in the equations have endpoint singularity. However, existing methods have the disadvantage of inconsistent collocation points. This inconsistency complicates the implementation of such methods, particularly for large-scale problems. To overcome this drawback, this study proposes another Sinc-collocation methods with consistent collocation points. The results of a theoretical error analysis show that the proposed methods have the same convergence property as existing methods. Numerical experiments suggest the superiority of the proposed methods in terms of implementation and computational cost. |
| title | Sinc-collocation methods with consistent collocation points for Fredholm integral equations of the second kind |
| topic | Numerical Analysis 65R20 |
| url | https://arxiv.org/abs/2301.12692 |