{"paper":{"title":"Fast Runge-Kutta approximation of inhomogeneous parabolic equations","license":"","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Achim Sch\\\"adle, Cesar Palencia, Christian Lubich, Mar\\'ia L\\'opez-Fern\\'andez","submitted_at":"2005-04-22T14:39:51Z","abstract_excerpt":"The result after $N$ steps of an implicit Runge-Kutta time discretization of an inhomogeneous linear parabolic differential equation is computed, up to accuracy $\\epsilon$, by solving only $$O\\Big(\\log N \\log \\frac1\\epsilon \\Big) $$ linear systems of equations. We derive, analyse, and numerically illustrate this fast algorithm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504466","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"}