{"paper":{"title":"Reliability of the time splitting Fourier method for singular solutions in quantum fluids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Marco Caliari, Simone Zuccher","submitted_at":"2016-03-16T10:40:45Z","abstract_excerpt":"We extensively study the numerical accuracy of the well-known time splitting Fourier spectral method for the approximation of singular solutions of the Gross-Pitaevskii equation. In particular, we explore its capability of preserving a steady-state vortex solution, whose density profile is approximated by a very accurate diagonal Pad\\'e expansion of order 8, here explicitly derived for the first time. Although the Fourier spectral method turns out to be only slightly more accurate than a time splitting finite difference scheme, the former is reliable and efficient. Moreover, at a post-processi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05022","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}