{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:XXRB2726CZWJG3Y3NIVKCXTSPM","short_pith_number":"pith:XXRB2726","schema_version":"1.0","canonical_sha256":"bde21d7f5e166c936f1b6a2aa15e727b0dfcb3a9e26407dc98dd00f0ffb3ec4a","source":{"kind":"arxiv","id":"1304.3805","version":2},"attestation_state":"computed","paper":{"title":"Stability theory for difference approximations of some dispersive shallow water equations and application to thin film flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jean-Paul Vila, Pascal Noble","submitted_at":"2013-04-13T13:17:44Z","abstract_excerpt":"In this paper, we study the stability of various difference approximations of the Euler-Korteweg equations. This system of evolution PDEs is a classical isentropic Euler system perturbed by a dispersive (third order) term. The Euler equations are discretized with a classical scheme (e.g. Roe, Rusanov or Lax-Friedrichs scheme) whereas the dispersive term is discretized with centered finite differences. We first prove that a certain amount of numerical viscosity is needed for a difference scheme to be stable in the Von Neumann sense. Then we consider the entropy stability of difference approxima"},"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":"1304.3805","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-04-13T13:17:44Z","cross_cats_sorted":[],"title_canon_sha256":"5b14fd3b148509dc029b99fa8b60da55359341256d18c609c46068029e925917","abstract_canon_sha256":"0d7966306e92c3ada7b094aba69deaadc6b6008f8ef1f6105a56eebda2995eb8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:00:49.604627Z","signature_b64":"ZRGQI20KT9B47rr7wpUUHFFx0LQaYbyscs8+A3wfaZv+LwLsmBxYLCnkxK6OYpvOIU8TfgdPbPDJ0h0GHQBaAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bde21d7f5e166c936f1b6a2aa15e727b0dfcb3a9e26407dc98dd00f0ffb3ec4a","last_reissued_at":"2026-05-18T03:00:49.603812Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:00:49.603812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability theory for difference approximations of some dispersive shallow water equations and application to thin film flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jean-Paul Vila, Pascal Noble","submitted_at":"2013-04-13T13:17:44Z","abstract_excerpt":"In this paper, we study the stability of various difference approximations of the Euler-Korteweg equations. This system of evolution PDEs is a classical isentropic Euler system perturbed by a dispersive (third order) term. The Euler equations are discretized with a classical scheme (e.g. Roe, Rusanov or Lax-Friedrichs scheme) whereas the dispersive term is discretized with centered finite differences. We first prove that a certain amount of numerical viscosity is needed for a difference scheme to be stable in the Von Neumann sense. Then we consider the entropy stability of difference approxima"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3805","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":"1304.3805","created_at":"2026-05-18T03:00:49.603916+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.3805v2","created_at":"2026-05-18T03:00:49.603916+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3805","created_at":"2026-05-18T03:00:49.603916+00:00"},{"alias_kind":"pith_short_12","alias_value":"XXRB2726CZWJ","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_16","alias_value":"XXRB2726CZWJG3Y3","created_at":"2026-05-18T12:28:06.772260+00:00"},{"alias_kind":"pith_short_8","alias_value":"XXRB2726","created_at":"2026-05-18T12:28:06.772260+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/XXRB2726CZWJG3Y3NIVKCXTSPM","json":"https://pith.science/pith/XXRB2726CZWJG3Y3NIVKCXTSPM.json","graph_json":"https://pith.science/api/pith-number/XXRB2726CZWJG3Y3NIVKCXTSPM/graph.json","events_json":"https://pith.science/api/pith-number/XXRB2726CZWJG3Y3NIVKCXTSPM/events.json","paper":"https://pith.science/paper/XXRB2726"},"agent_actions":{"view_html":"https://pith.science/pith/XXRB2726CZWJG3Y3NIVKCXTSPM","download_json":"https://pith.science/pith/XXRB2726CZWJG3Y3NIVKCXTSPM.json","view_paper":"https://pith.science/paper/XXRB2726","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.3805&json=true","fetch_graph":"https://pith.science/api/pith-number/XXRB2726CZWJG3Y3NIVKCXTSPM/graph.json","fetch_events":"https://pith.science/api/pith-number/XXRB2726CZWJG3Y3NIVKCXTSPM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XXRB2726CZWJG3Y3NIVKCXTSPM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XXRB2726CZWJG3Y3NIVKCXTSPM/action/storage_attestation","attest_author":"https://pith.science/pith/XXRB2726CZWJG3Y3NIVKCXTSPM/action/author_attestation","sign_citation":"https://pith.science/pith/XXRB2726CZWJG3Y3NIVKCXTSPM/action/citation_signature","submit_replication":"https://pith.science/pith/XXRB2726CZWJG3Y3NIVKCXTSPM/action/replication_record"}},"created_at":"2026-05-18T03:00:49.603916+00:00","updated_at":"2026-05-18T03:00:49.603916+00:00"}