{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:AXM5WNFG6HK4VI3AIQA5UMNVCL","short_pith_number":"pith:AXM5WNFG","schema_version":"1.0","canonical_sha256":"05d9db34a6f1d5caa3604401da31b512ea8cd5d22608956faffd18a0d9bdac04","source":{"kind":"arxiv","id":"1301.2643","version":1},"attestation_state":"computed","paper":{"title":"Second-order LOD multigrid method for multidimensional Riesz fractional diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Minghua Chen, Weihua Deng, Xiao Cheng, Yantao Wang","submitted_at":"2013-01-12T03:26:09Z","abstract_excerpt":"We propose a locally one dimensional (LOD) finite difference method for multidimensional Riesz fractional diffusion equation with variable coefficients on a finite domain. The numerical method is second-order convergent in both space and time directions, and its unconditional stability is strictly proved. Comparing with the popular first-order finite difference method for fractional operator, the form of obtained matrix algebraic equation is changed from $(I-A)u^{k+1}=u^k+b^{k+1}$ to $(I-{\\widetilde A})u^{k+1}=(I+{\\widetilde B})u^k+{\\tilde b}^{k+1/2}$; the three matrices $A$, ${\\widetilde A}$ "},"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":"1301.2643","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-01-12T03:26:09Z","cross_cats_sorted":[],"title_canon_sha256":"efcc5936d5df86c7638fbf411332b4cb36ad9ef902c89bb2389d3ce6a2171537","abstract_canon_sha256":"c86f59df0e188aec5c221622623e077eca6e720109c664603e55fd95fa58fadd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:29.145626Z","signature_b64":"ZOa2IOeybzdQMimxDxbhsXXOwqj3AMF6j4Wa7ZU9nIDht6sFNi5bhBnJCcOClPL/fRjgqGV1T2/ZfmI0t1PdCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05d9db34a6f1d5caa3604401da31b512ea8cd5d22608956faffd18a0d9bdac04","last_reissued_at":"2026-05-18T02:42:29.144677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:29.144677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second-order LOD multigrid method for multidimensional Riesz fractional diffusion equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Minghua Chen, Weihua Deng, Xiao Cheng, Yantao Wang","submitted_at":"2013-01-12T03:26:09Z","abstract_excerpt":"We propose a locally one dimensional (LOD) finite difference method for multidimensional Riesz fractional diffusion equation with variable coefficients on a finite domain. The numerical method is second-order convergent in both space and time directions, and its unconditional stability is strictly proved. Comparing with the popular first-order finite difference method for fractional operator, the form of obtained matrix algebraic equation is changed from $(I-A)u^{k+1}=u^k+b^{k+1}$ to $(I-{\\widetilde A})u^{k+1}=(I+{\\widetilde B})u^k+{\\tilde b}^{k+1/2}$; the three matrices $A$, ${\\widetilde A}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2643","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":"1301.2643","created_at":"2026-05-18T02:42:29.144835+00:00"},{"alias_kind":"arxiv_version","alias_value":"1301.2643v1","created_at":"2026-05-18T02:42:29.144835+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2643","created_at":"2026-05-18T02:42:29.144835+00:00"},{"alias_kind":"pith_short_12","alias_value":"AXM5WNFG6HK4","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"AXM5WNFG6HK4VI3A","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"AXM5WNFG","created_at":"2026-05-18T12:27:38.830355+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/AXM5WNFG6HK4VI3AIQA5UMNVCL","json":"https://pith.science/pith/AXM5WNFG6HK4VI3AIQA5UMNVCL.json","graph_json":"https://pith.science/api/pith-number/AXM5WNFG6HK4VI3AIQA5UMNVCL/graph.json","events_json":"https://pith.science/api/pith-number/AXM5WNFG6HK4VI3AIQA5UMNVCL/events.json","paper":"https://pith.science/paper/AXM5WNFG"},"agent_actions":{"view_html":"https://pith.science/pith/AXM5WNFG6HK4VI3AIQA5UMNVCL","download_json":"https://pith.science/pith/AXM5WNFG6HK4VI3AIQA5UMNVCL.json","view_paper":"https://pith.science/paper/AXM5WNFG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1301.2643&json=true","fetch_graph":"https://pith.science/api/pith-number/AXM5WNFG6HK4VI3AIQA5UMNVCL/graph.json","fetch_events":"https://pith.science/api/pith-number/AXM5WNFG6HK4VI3AIQA5UMNVCL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AXM5WNFG6HK4VI3AIQA5UMNVCL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AXM5WNFG6HK4VI3AIQA5UMNVCL/action/storage_attestation","attest_author":"https://pith.science/pith/AXM5WNFG6HK4VI3AIQA5UMNVCL/action/author_attestation","sign_citation":"https://pith.science/pith/AXM5WNFG6HK4VI3AIQA5UMNVCL/action/citation_signature","submit_replication":"https://pith.science/pith/AXM5WNFG6HK4VI3AIQA5UMNVCL/action/replication_record"}},"created_at":"2026-05-18T02:42:29.144835+00:00","updated_at":"2026-05-18T02:42:29.144835+00:00"}