{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:FVWNZ3OOKYNHUIJBWTBTZH22YM","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"88cfc3f4bc422f20dd20a41ac2372610902841f58a6ada8d45fb4173c02ef301","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-08-06T01:49:05Z","title_canon_sha256":"b14bc51c33f141f624b32f37d4e7fdc3b42c1bf0bd0c3c2eb218ee4590e52f84"},"schema_version":"1.0","source":{"id":"2108.02910","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.02910","created_at":"2026-07-05T03:03:43Z"},{"alias_kind":"arxiv_version","alias_value":"2108.02910v1","created_at":"2026-07-05T03:03:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.02910","created_at":"2026-07-05T03:03:43Z"},{"alias_kind":"pith_short_12","alias_value":"FVWNZ3OOKYNH","created_at":"2026-07-05T03:03:43Z"},{"alias_kind":"pith_short_16","alias_value":"FVWNZ3OOKYNHUIJB","created_at":"2026-07-05T03:03:43Z"},{"alias_kind":"pith_short_8","alias_value":"FVWNZ3OO","created_at":"2026-07-05T03:03:43Z"}],"graph_snapshots":[{"event_id":"sha256:87050b226002228a63bafa468eca733f82803ce78d7c9a2ada6e69777fc6041c","target":"graph","created_at":"2026-07-05T03:03:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2108.02910/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Variable steps implicit-explicit multistep methods for PDEs have been presented in [17], where the zero-stability is studied for ODEs; however, the stability analysis still remains an open question for PDEs. Based on the idea of linear multistep methods, we present a simple weighted and shifted BDF2 methods with variable steps for the parabolic problems, which serve as a bridge between BDF2 and Crank-Nicolson scheme. The contributions of this paper are as follows: we first prove that the optimal adjacent time-step ratios for the weighted and shifted BDF2, which greatly improve the maximum time","authors_text":"Fan Yu, Minghua Chen, Qingdong Zhang","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-08-06T01:49:05Z","title":"Weighted and shifted BDF2 methods on variable grids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.02910","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:5445d98f6ba0d452bdda1db335e395d4c8a552f05c789994c08e9fee30f4f9fc","target":"record","created_at":"2026-07-05T03:03:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"88cfc3f4bc422f20dd20a41ac2372610902841f58a6ada8d45fb4173c02ef301","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-08-06T01:49:05Z","title_canon_sha256":"b14bc51c33f141f624b32f37d4e7fdc3b42c1bf0bd0c3c2eb218ee4590e52f84"},"schema_version":"1.0","source":{"id":"2108.02910","kind":"arxiv","version":1}},"canonical_sha256":"2d6cdcedce561a7a2121b4c33c9f5ac323430eb15ff70f9cadd1307bbb1c2bc5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d6cdcedce561a7a2121b4c33c9f5ac323430eb15ff70f9cadd1307bbb1c2bc5","first_computed_at":"2026-07-05T03:03:43.521076Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:03:43.521076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wUFhF27hMnfVsw+SBMeFgMvInpFA4Oot6r5jGxO8WU8WliV2/bVLPXWMQfhqyFoGnKwtTCZU0P3Te6fhPB4jAw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:03:43.521536Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.02910","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5445d98f6ba0d452bdda1db335e395d4c8a552f05c789994c08e9fee30f4f9fc","sha256:87050b226002228a63bafa468eca733f82803ce78d7c9a2ada6e69777fc6041c"],"state_sha256":"3274ecd25494fba8d1d3e76943d4fa3c4c5d6b7ca4e9b8b261b2d537a625898c"}