{"paper":{"title":"Error analysis of the Strang splitting for the 3D semilinear wave equation with finite-energy data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Maximilian Ruff","submitted_at":"2025-03-17T12:48:52Z","abstract_excerpt":"We study a variant of the Strang splitting for the time integration of the semilinear wave equation under the finite-energy condition on the torus $\\mathbb{T}^3$. In the case of a cubic nonlinearity, we show almost second-order convergence in $L^2$ and almost first-order convergence in $H^1$. If the nonlinearity has a quartic form instead, we show an analogous convergence results, where the order is reduced by $1/2$ in both cases. To our knowledge these are the best convergence results available for the 3D cubic and quartic wave equations under the finite-energy condition. Our approach relies "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.13126","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.13126/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}