{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:VPQ5KB3V2CN5655NTVN7I64XIV","short_pith_number":"pith:VPQ5KB3V","schema_version":"1.0","canonical_sha256":"abe1d50775d09bdf77ad9d5bf47b974543fc92abe438c76a6e33d86012cc86bd","source":{"kind":"arxiv","id":"1305.5481","version":2},"attestation_state":"computed","paper":{"title":"Rosenbrock-Krylov Methods for Large Systems of Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Adrian Sandu, Paul Tranquilli","submitted_at":"2013-05-23T16:45:29Z","abstract_excerpt":"This paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems. The new family, called Rosenbrock-Krylov (Rosenbrock-K), is well suited for solving large scale systems of ODEs or semi-discrete PDEs. The time discretization and the Krylov space approximation are treated as a single computational process, and the Krylov space properties are an integral part of the new Rosenbrock-K order condition theory developed herein. Consequently, Rosenbrock-K methods require a small number of basis vectors determined solely by the temporal order of accu"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1305.5481","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-05-23T16:45:29Z","cross_cats_sorted":[],"title_canon_sha256":"e9b351db45ddcc88395dbb65b7def7bf28b00af51e2f68ffba80f7e0f694b16b","abstract_canon_sha256":"662e597249e7a190c642ba4ad16f725b357e7f3e0e4d01e436c1d69b3636ab26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:29.442200Z","signature_b64":"w92kIDQa3su2Fuel2eJCOM8pwX/bL78BxmBccFOAOktzjZlTOsvc6N5qJSVvDfxNIJzzg3I7e4BL0UvAzILyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abe1d50775d09bdf77ad9d5bf47b974543fc92abe438c76a6e33d86012cc86bd","last_reissued_at":"2026-05-18T02:28:29.441771Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:29.441771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rosenbrock-Krylov Methods for Large Systems of Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Adrian Sandu, Paul Tranquilli","submitted_at":"2013-05-23T16:45:29Z","abstract_excerpt":"This paper develops a new class of Rosenbrock-type integrators based on a Krylov space solution of the linear systems. The new family, called Rosenbrock-Krylov (Rosenbrock-K), is well suited for solving large scale systems of ODEs or semi-discrete PDEs. The time discretization and the Krylov space approximation are treated as a single computational process, and the Krylov space properties are an integral part of the new Rosenbrock-K order condition theory developed herein. Consequently, Rosenbrock-K methods require a small number of basis vectors determined solely by the temporal order of accu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5481","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.5481","created_at":"2026-05-18T02:28:29.441835+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.5481v2","created_at":"2026-05-18T02:28:29.441835+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5481","created_at":"2026-05-18T02:28:29.441835+00:00"},{"alias_kind":"pith_short_12","alias_value":"VPQ5KB3V2CN5","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_16","alias_value":"VPQ5KB3V2CN5655N","created_at":"2026-05-18T12:28:04.890932+00:00"},{"alias_kind":"pith_short_8","alias_value":"VPQ5KB3V","created_at":"2026-05-18T12:28:04.890932+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VPQ5KB3V2CN5655NTVN7I64XIV","json":"https://pith.science/pith/VPQ5KB3V2CN5655NTVN7I64XIV.json","graph_json":"https://pith.science/api/pith-number/VPQ5KB3V2CN5655NTVN7I64XIV/graph.json","events_json":"https://pith.science/api/pith-number/VPQ5KB3V2CN5655NTVN7I64XIV/events.json","paper":"https://pith.science/paper/VPQ5KB3V"},"agent_actions":{"view_html":"https://pith.science/pith/VPQ5KB3V2CN5655NTVN7I64XIV","download_json":"https://pith.science/pith/VPQ5KB3V2CN5655NTVN7I64XIV.json","view_paper":"https://pith.science/paper/VPQ5KB3V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.5481&json=true","fetch_graph":"https://pith.science/api/pith-number/VPQ5KB3V2CN5655NTVN7I64XIV/graph.json","fetch_events":"https://pith.science/api/pith-number/VPQ5KB3V2CN5655NTVN7I64XIV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VPQ5KB3V2CN5655NTVN7I64XIV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VPQ5KB3V2CN5655NTVN7I64XIV/action/storage_attestation","attest_author":"https://pith.science/pith/VPQ5KB3V2CN5655NTVN7I64XIV/action/author_attestation","sign_citation":"https://pith.science/pith/VPQ5KB3V2CN5655NTVN7I64XIV/action/citation_signature","submit_replication":"https://pith.science/pith/VPQ5KB3V2CN5655NTVN7I64XIV/action/replication_record"}},"created_at":"2026-05-18T02:28:29.441835+00:00","updated_at":"2026-05-18T02:28:29.441835+00:00"}