{"paper":{"title":"An L-Stable Sequential Two-Stage Fourth-Order Method with ADER Trajectory Derivatives for Stiff Transport--Relaxation Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Yangnan Su, Zhixin Huo","submitted_at":"2026-08-04T07:29:51Z","abstract_excerpt":"A fully implicit two-stage fourth-order two-derivative time discretization was introduced previously as a temporal method. This paper closes that sequential integrator for stiff transport--relaxation equations by pairing a conservative finite-volume residual $\\mathcal L_h$ with its discrete trajectory derivative $\\mathcal G_h^{\\rm tr}=D\\mathcal L_h\\,\\mathcal L_h$. An ADER/Cauchy--Kowalevski predictor provides interface states and physical time derivatives; differentiating the same numerical flux and taking shared face differences yields a conservative approximation $\\widetilde{\\mathcal G}_h$. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03256","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.03256/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"}