{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:IMSRUJOEWBF7KAQUEF437T3A42","short_pith_number":"pith:IMSRUJOE","schema_version":"1.0","canonical_sha256":"43251a25c4b04bf502142179bfcf60e6b0e19c3196aefdec2091b869d434a439","source":{"kind":"arxiv","id":"1507.06484","version":1},"attestation_state":"computed","paper":{"title":"Numerical solution of Volterra integral equations of the first kind with discontinuous kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Aleksandr Tynda, Denis Sidorov, Ildar Muftahov","submitted_at":"2015-07-23T13:11:31Z","abstract_excerpt":"We propose the numerical methods for solution of the weakly regular linear and nonlinear evolutionary (Volterra) integral equation of the first kind. The kernels of such equations have jump discontinuities along the continuous curves (endogenous delays) which starts at the origin. In order to linearize these equations we use the modified Newton-Kantorovich iterative process. Then for linear equations we propose two direct quadrature methods based on the piecewise constant and piecewise linear approximation of the exact solution. The accuracy of proposed numerical methods is $\\mathcal{O}(1/N)$ "},"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":"1507.06484","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2015-07-23T13:11:31Z","cross_cats_sorted":[],"title_canon_sha256":"cab7a495b58da540f5f21d114b7592e33813c36e0edf086235c278e8a19cde40","abstract_canon_sha256":"cb53ba986c32f1e7facc825b3e72f1113970c82750ce65dc86475373dbfe9ecf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:24.829731Z","signature_b64":"p9BWg+Jf5jBD9516hPKSsIIbyFzgyQ3+henml0T0bra2kcD77Xf/erntcUUwVEd56oRdA6wtl3tveMzQhg6UCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43251a25c4b04bf502142179bfcf60e6b0e19c3196aefdec2091b869d434a439","last_reissued_at":"2026-05-18T01:36:24.829260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:24.829260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical solution of Volterra integral equations of the first kind with discontinuous kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Aleksandr Tynda, Denis Sidorov, Ildar Muftahov","submitted_at":"2015-07-23T13:11:31Z","abstract_excerpt":"We propose the numerical methods for solution of the weakly regular linear and nonlinear evolutionary (Volterra) integral equation of the first kind. The kernels of such equations have jump discontinuities along the continuous curves (endogenous delays) which starts at the origin. In order to linearize these equations we use the modified Newton-Kantorovich iterative process. Then for linear equations we propose two direct quadrature methods based on the piecewise constant and piecewise linear approximation of the exact solution. The accuracy of proposed numerical methods is $\\mathcal{O}(1/N)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06484","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":"1507.06484","created_at":"2026-05-18T01:36:24.829348+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.06484v1","created_at":"2026-05-18T01:36:24.829348+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06484","created_at":"2026-05-18T01:36:24.829348+00:00"},{"alias_kind":"pith_short_12","alias_value":"IMSRUJOEWBF7","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"IMSRUJOEWBF7KAQU","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"IMSRUJOE","created_at":"2026-05-18T12:29:25.134429+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/IMSRUJOEWBF7KAQUEF437T3A42","json":"https://pith.science/pith/IMSRUJOEWBF7KAQUEF437T3A42.json","graph_json":"https://pith.science/api/pith-number/IMSRUJOEWBF7KAQUEF437T3A42/graph.json","events_json":"https://pith.science/api/pith-number/IMSRUJOEWBF7KAQUEF437T3A42/events.json","paper":"https://pith.science/paper/IMSRUJOE"},"agent_actions":{"view_html":"https://pith.science/pith/IMSRUJOEWBF7KAQUEF437T3A42","download_json":"https://pith.science/pith/IMSRUJOEWBF7KAQUEF437T3A42.json","view_paper":"https://pith.science/paper/IMSRUJOE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.06484&json=true","fetch_graph":"https://pith.science/api/pith-number/IMSRUJOEWBF7KAQUEF437T3A42/graph.json","fetch_events":"https://pith.science/api/pith-number/IMSRUJOEWBF7KAQUEF437T3A42/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IMSRUJOEWBF7KAQUEF437T3A42/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IMSRUJOEWBF7KAQUEF437T3A42/action/storage_attestation","attest_author":"https://pith.science/pith/IMSRUJOEWBF7KAQUEF437T3A42/action/author_attestation","sign_citation":"https://pith.science/pith/IMSRUJOEWBF7KAQUEF437T3A42/action/citation_signature","submit_replication":"https://pith.science/pith/IMSRUJOEWBF7KAQUEF437T3A42/action/replication_record"}},"created_at":"2026-05-18T01:36:24.829348+00:00","updated_at":"2026-05-18T01:36:24.829348+00:00"}