{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:DALRFTX22YKNZLMX5NQOSSCVTZ","short_pith_number":"pith:DALRFTX2","schema_version":"1.0","canonical_sha256":"181712cefad614dcad97eb60e948559e4a6cc1fe9e24dd3e94bfef8a6a1cf0da","source":{"kind":"arxiv","id":"2002.03655","version":1},"attestation_state":"computed","paper":{"title":"Fast and High-order Accuracy Numerical Methods for Time-Dependent Nonlocal Problems in $\\mathbb{R}^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Michael K. Ng, Minghua Chen, Rongjun Cao, Yu-Jiang Wu","submitted_at":"2020-02-10T11:05:49Z","abstract_excerpt":"In this paper, we study the Crank-Nicolson method for temporal dimension and the piecewise quadratic polynomial collocation method for spatial dimensions of time-dependent nonlocal problems. The new theoretical results of such discretization are that the proposed numerical method is unconditionally stable and its global truncation error is of $\\mathcal{O}\\left(\\tau^2+h^{4-\\gamma}\\right)$ with $0<\\gamma<1$, where $\\tau$ and $h$ are the discretization sizes in the temporal and spatial dimensions respectively. Also we develop the conjugate gradient squared method to solving the resulting discreti"},"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":"2002.03655","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2020-02-10T11:05:49Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"d1b0ac55324568e3ee74b19a125c81374e29cab24eb04a71c21df92bc5bdae8c","abstract_canon_sha256":"26a28be5c0bf7b72c31029f48389f88fbfc74200836033788f808a8e25d8e390"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:13:57.845299Z","signature_b64":"iuCCl2XY1vMqT6U27/c8ris/FOk9dkNHCWiTG9Zeeb8Y6lZh3saNncbdfkjWVCtAb34ATn27XQMjlbT9o1wlBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"181712cefad614dcad97eb60e948559e4a6cc1fe9e24dd3e94bfef8a6a1cf0da","last_reissued_at":"2026-07-05T01:13:57.844860Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:13:57.844860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fast and High-order Accuracy Numerical Methods for Time-Dependent Nonlocal Problems in $\\mathbb{R}^2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Michael K. Ng, Minghua Chen, Rongjun Cao, Yu-Jiang Wu","submitted_at":"2020-02-10T11:05:49Z","abstract_excerpt":"In this paper, we study the Crank-Nicolson method for temporal dimension and the piecewise quadratic polynomial collocation method for spatial dimensions of time-dependent nonlocal problems. The new theoretical results of such discretization are that the proposed numerical method is unconditionally stable and its global truncation error is of $\\mathcal{O}\\left(\\tau^2+h^{4-\\gamma}\\right)$ with $0<\\gamma<1$, where $\\tau$ and $h$ are the discretization sizes in the temporal and spatial dimensions respectively. Also we develop the conjugate gradient squared method to solving the resulting discreti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.03655","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/2002.03655/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2002.03655","created_at":"2026-07-05T01:13:57.844919+00:00"},{"alias_kind":"arxiv_version","alias_value":"2002.03655v1","created_at":"2026-07-05T01:13:57.844919+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.03655","created_at":"2026-07-05T01:13:57.844919+00:00"},{"alias_kind":"pith_short_12","alias_value":"DALRFTX22YKN","created_at":"2026-07-05T01:13:57.844919+00:00"},{"alias_kind":"pith_short_16","alias_value":"DALRFTX22YKNZLMX","created_at":"2026-07-05T01:13:57.844919+00:00"},{"alias_kind":"pith_short_8","alias_value":"DALRFTX2","created_at":"2026-07-05T01:13:57.844919+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/DALRFTX22YKNZLMX5NQOSSCVTZ","json":"https://pith.science/pith/DALRFTX22YKNZLMX5NQOSSCVTZ.json","graph_json":"https://pith.science/api/pith-number/DALRFTX22YKNZLMX5NQOSSCVTZ/graph.json","events_json":"https://pith.science/api/pith-number/DALRFTX22YKNZLMX5NQOSSCVTZ/events.json","paper":"https://pith.science/paper/DALRFTX2"},"agent_actions":{"view_html":"https://pith.science/pith/DALRFTX22YKNZLMX5NQOSSCVTZ","download_json":"https://pith.science/pith/DALRFTX22YKNZLMX5NQOSSCVTZ.json","view_paper":"https://pith.science/paper/DALRFTX2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2002.03655&json=true","fetch_graph":"https://pith.science/api/pith-number/DALRFTX22YKNZLMX5NQOSSCVTZ/graph.json","fetch_events":"https://pith.science/api/pith-number/DALRFTX22YKNZLMX5NQOSSCVTZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DALRFTX22YKNZLMX5NQOSSCVTZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DALRFTX22YKNZLMX5NQOSSCVTZ/action/storage_attestation","attest_author":"https://pith.science/pith/DALRFTX22YKNZLMX5NQOSSCVTZ/action/author_attestation","sign_citation":"https://pith.science/pith/DALRFTX22YKNZLMX5NQOSSCVTZ/action/citation_signature","submit_replication":"https://pith.science/pith/DALRFTX22YKNZLMX5NQOSSCVTZ/action/replication_record"}},"created_at":"2026-07-05T01:13:57.844919+00:00","updated_at":"2026-07-05T01:13:57.844919+00:00"}