Improvement of Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind and their theoretical analysis
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914089999007744 |
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| author | Okayama, Tomoaki |
| author_facet | Okayama, Tomoaki |
| contents | Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind were proposed independently by multiple authors: by Shamloo et al. in 2012 and by Mesgarani and Mollapourasl in 2013. Their theoretical analyses and numerical experiments suggest that the presented methods can attain root-exponential convergence. However, their convergence has not been strictly proved. This study improves these methods to facilitate implementation, and provides a convergence theorem for the improved method. For the same equations, another Sinc-collocation method was proposed in 2016 by John and Ogbonna, which is regarded as an improvement to the variable transformation employed by Shamloo et al. It may attain a higher rate than the previous methods, but its convergence has not yet been proved. Therefore, this study improves it to facilitate implementation, and provides a convergence theorem for the improved method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_11569 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improvement of Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind and their theoretical analysis Okayama, Tomoaki Numerical Analysis 65R20 Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind were proposed independently by multiple authors: by Shamloo et al. in 2012 and by Mesgarani and Mollapourasl in 2013. Their theoretical analyses and numerical experiments suggest that the presented methods can attain root-exponential convergence. However, their convergence has not been strictly proved. This study improves these methods to facilitate implementation, and provides a convergence theorem for the improved method. For the same equations, another Sinc-collocation method was proposed in 2016 by John and Ogbonna, which is regarded as an improvement to the variable transformation employed by Shamloo et al. It may attain a higher rate than the previous methods, but its convergence has not yet been proved. Therefore, this study improves it to facilitate implementation, and provides a convergence theorem for the improved method. |
| title | Improvement of Sinc-collocation methods for Volterra-Fredholm integral equations of the second kind and their theoretical analysis |
| topic | Numerical Analysis 65R20 |
| url | https://arxiv.org/abs/2503.11569 |