{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:RAJUTXO52ZYRUKRIXHLULATIPJ","short_pith_number":"pith:RAJUTXO5","schema_version":"1.0","canonical_sha256":"881349ddddd6711a2a28b9d74582687a560c019ae7280e7d1b479542f8cd5059","source":{"kind":"arxiv","id":"1810.12420","version":1},"attestation_state":"computed","paper":{"title":"Spectral approximation of a variable coefficient fractional diffusion equation in one space dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hong Wang, V. J. Ervin, Xiangcheng Zheng","submitted_at":"2018-10-29T21:37:12Z","abstract_excerpt":"In this article we consider the approximation of a variable coefficient (two-sided) fractional diffusion equation (FDE), having unknown $u$. By introducing an intermediate unknown, $q$, the variable coefficient FDE is rewritten as a lower order, constant coefficient FDE. A spectral approximation scheme, using Jacobi polynomials, is presented for the approximation of $q$, $q_{N}$. The approximate solution to $u$, $u_{N}$, is obtained by post processing $q_{N}$. An a priori error analysis is given for $(q \\, - \\, q_{N})$ and $(u \\, - \\, u_{N})$. Two numerical experiments are presented whose resu"},"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":"1810.12420","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-29T21:37:12Z","cross_cats_sorted":[],"title_canon_sha256":"bffa701448859a76e9f7e505585d606b604c21112f385940e1856dd67e202840","abstract_canon_sha256":"43789ea9c725830cd666db7a2488550eeb3ec5aa79123167fe5c1a216b8d7d06"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:02.728639Z","signature_b64":"gZQ+/e2IRE6bALem4X5Az1sB5AMyRVjXpZRrMbTDZONmj9Ms70d3UFf4KP2AeQTFRFyO1waVbcbsNVwSM8VACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"881349ddddd6711a2a28b9d74582687a560c019ae7280e7d1b479542f8cd5059","last_reissued_at":"2026-05-18T00:02:02.728076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:02.728076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral approximation of a variable coefficient fractional diffusion equation in one space dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hong Wang, V. J. Ervin, Xiangcheng Zheng","submitted_at":"2018-10-29T21:37:12Z","abstract_excerpt":"In this article we consider the approximation of a variable coefficient (two-sided) fractional diffusion equation (FDE), having unknown $u$. By introducing an intermediate unknown, $q$, the variable coefficient FDE is rewritten as a lower order, constant coefficient FDE. A spectral approximation scheme, using Jacobi polynomials, is presented for the approximation of $q$, $q_{N}$. The approximate solution to $u$, $u_{N}$, is obtained by post processing $q_{N}$. An a priori error analysis is given for $(q \\, - \\, q_{N})$ and $(u \\, - \\, u_{N})$. Two numerical experiments are presented whose resu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12420","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":"1810.12420","created_at":"2026-05-18T00:02:02.728167+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.12420v1","created_at":"2026-05-18T00:02:02.728167+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.12420","created_at":"2026-05-18T00:02:02.728167+00:00"},{"alias_kind":"pith_short_12","alias_value":"RAJUTXO52ZYR","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_16","alias_value":"RAJUTXO52ZYRUKRI","created_at":"2026-05-18T12:32:50.500415+00:00"},{"alias_kind":"pith_short_8","alias_value":"RAJUTXO5","created_at":"2026-05-18T12:32:50.500415+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/RAJUTXO52ZYRUKRIXHLULATIPJ","json":"https://pith.science/pith/RAJUTXO52ZYRUKRIXHLULATIPJ.json","graph_json":"https://pith.science/api/pith-number/RAJUTXO52ZYRUKRIXHLULATIPJ/graph.json","events_json":"https://pith.science/api/pith-number/RAJUTXO52ZYRUKRIXHLULATIPJ/events.json","paper":"https://pith.science/paper/RAJUTXO5"},"agent_actions":{"view_html":"https://pith.science/pith/RAJUTXO52ZYRUKRIXHLULATIPJ","download_json":"https://pith.science/pith/RAJUTXO52ZYRUKRIXHLULATIPJ.json","view_paper":"https://pith.science/paper/RAJUTXO5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.12420&json=true","fetch_graph":"https://pith.science/api/pith-number/RAJUTXO52ZYRUKRIXHLULATIPJ/graph.json","fetch_events":"https://pith.science/api/pith-number/RAJUTXO52ZYRUKRIXHLULATIPJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RAJUTXO52ZYRUKRIXHLULATIPJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RAJUTXO52ZYRUKRIXHLULATIPJ/action/storage_attestation","attest_author":"https://pith.science/pith/RAJUTXO52ZYRUKRIXHLULATIPJ/action/author_attestation","sign_citation":"https://pith.science/pith/RAJUTXO52ZYRUKRIXHLULATIPJ/action/citation_signature","submit_replication":"https://pith.science/pith/RAJUTXO52ZYRUKRIXHLULATIPJ/action/replication_record"}},"created_at":"2026-05-18T00:02:02.728167+00:00","updated_at":"2026-05-18T00:02:02.728167+00:00"}