{"paper":{"title":"A stable fast time-stepping method for fractional integral and derivative operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Fanhai Zeng, Ian Turner, Kevin Burrage","submitted_at":"2017-03-16T06:28:07Z","abstract_excerpt":"A unified fast time-stepping method for both fractional integral and derivative operators is proposed. The fractional operator is decomposed into a local part with memory length $\\Delta T$ and a history part, where the local part is approximated by the direct convolution method and the history part is approximated by a fast memory-saving method. The fast method has $O(n_0+\\sum_{\\ell}^L{q}_{\\alpha}(N_{\\ell}))$ active memory and $O(n_0n_T+ (n_T-n_0)\\sum_{\\ell}^L{q}_{\\alpha}(N_{\\ell}))$ operations, where $L=\\log(n_T-n_0)$, $n_0={\\Delta T}/\\tau,n_T=T/\\tau$, $\\tau$ is the stepsize, $T$ is the final"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05480","kind":"arxiv","version":2},"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"}