{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/on-the-use-of-conformal-maps-for-the","title":"On the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods","arxiv_id":"1406.3320","date":"2014-06-12","proceeding":null,"authors":["Richard Mikael Slevinsky","Sheehan Olver"],"abstract":"We investigate the use of conformal maps for the acceleration of convergence of the trapezoidal rule and Sinc numerical methods. The conformal map is a polynomial adjustment to the $\\sinh$ map, and allows the treatment of a finite number of singularities in the complex plane. In the case where locations are unknown, the so-called Sinc-Pad\\'e approximants are used to provide approximate results. This adaptive method is shown to have almost the same convergence properties. We use the conformal maps to generate high accuracy solutions to several challenging integrals, nonlinear waves, and multidimensional integrals.","url_abs":"http://arxiv.org/abs/1406.3320v1","url_pdf":"http://arxiv.org/pdf/1406.3320v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"on-the-use-of-conformal-maps-for-the","repo_url":"https://github.com/MikaelSlevinsky/DEQuadrature.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"on-the-use-of-conformal-maps-for-the","repo_url":"https://github.com/pjgaudre/DESincEig.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}