{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3JGIZ6CUEVMQ6LZLFCSAAYZOBZ","short_pith_number":"pith:3JGIZ6CU","schema_version":"1.0","canonical_sha256":"da4c8cf85425590f2f2b28a400632e0e6e49c7c49315aee30b30e1255acde263","source":{"kind":"arxiv","id":"1307.0661","version":1},"attestation_state":"computed","paper":{"title":"Explicit exponential Runge-Kutta methods of high order for parabolic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.CA","authors_text":"Alexander Ostermann, Vu Thai Luan","submitted_at":"2013-07-02T10:16:47Z","abstract_excerpt":"Exponential Runge-Kutta methods constitute efficient integrators for semilinear stiff problems. So far, however, explicit exponential Runge-Kutta methods are available in the literature up to order 4 only. The aim of this paper is to construct a fifth-order method. For this purpose, we make use of a novel approach to derive the stiff order conditions for high-order exponential methods. This allows us to obtain the conditions for a method of order 5 in an elegant way. After stating the conditions, we first show that there does not exist an explicit exponential Runge-Kutta method of order 5 with"},"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":"1307.0661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-07-02T10:16:47Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"1741437a14039da3cd48bd3bef8ad1bf15a23d2d5e6aa9fde916b20af3e09365","abstract_canon_sha256":"f4559ea1f97fff15e51c1ccb3e61587004056c706c81a22282be5cd1e5cc29ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:20.150015Z","signature_b64":"qu6ULsNu00l7kDHvJhD2HL0DvIwqfuYATFHhlX0W7bsVfQFO6Mbj39R2i8POMc1WDEEkiMvRdmQtlhmj7Vs8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da4c8cf85425590f2f2b28a400632e0e6e49c7c49315aee30b30e1255acde263","last_reissued_at":"2026-05-18T01:12:20.149611Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:20.149611Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Explicit exponential Runge-Kutta methods of high order for parabolic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.CA","authors_text":"Alexander Ostermann, Vu Thai Luan","submitted_at":"2013-07-02T10:16:47Z","abstract_excerpt":"Exponential Runge-Kutta methods constitute efficient integrators for semilinear stiff problems. So far, however, explicit exponential Runge-Kutta methods are available in the literature up to order 4 only. The aim of this paper is to construct a fifth-order method. For this purpose, we make use of a novel approach to derive the stiff order conditions for high-order exponential methods. This allows us to obtain the conditions for a method of order 5 in an elegant way. After stating the conditions, we first show that there does not exist an explicit exponential Runge-Kutta method of order 5 with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0661","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1307.0661","created_at":"2026-05-18T01:12:20.149668+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.0661v1","created_at":"2026-05-18T01:12:20.149668+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0661","created_at":"2026-05-18T01:12:20.149668+00:00"},{"alias_kind":"pith_short_12","alias_value":"3JGIZ6CUEVMQ","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3JGIZ6CUEVMQ6LZL","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3JGIZ6CU","created_at":"2026-05-18T12:27:32.513160+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/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ","json":"https://pith.science/pith/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ.json","graph_json":"https://pith.science/api/pith-number/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ/graph.json","events_json":"https://pith.science/api/pith-number/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ/events.json","paper":"https://pith.science/paper/3JGIZ6CU"},"agent_actions":{"view_html":"https://pith.science/pith/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ","download_json":"https://pith.science/pith/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ.json","view_paper":"https://pith.science/paper/3JGIZ6CU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.0661&json=true","fetch_graph":"https://pith.science/api/pith-number/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ/graph.json","fetch_events":"https://pith.science/api/pith-number/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ/action/storage_attestation","attest_author":"https://pith.science/pith/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ/action/author_attestation","sign_citation":"https://pith.science/pith/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ/action/citation_signature","submit_replication":"https://pith.science/pith/3JGIZ6CUEVMQ6LZLFCSAAYZOBZ/action/replication_record"}},"created_at":"2026-05-18T01:12:20.149668+00:00","updated_at":"2026-05-18T01:12:20.149668+00:00"}