{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:36O2KC4JD43YDJIMY3BQS7JV5H","short_pith_number":"pith:36O2KC4J","schema_version":"1.0","canonical_sha256":"df9da50b891f3781a50cc6c3097d35e9e2e03538be6dddf538728543c36219d1","source":{"kind":"arxiv","id":"1103.0491","version":1},"attestation_state":"computed","paper":{"title":"Efficient approximation of the solution of certain nonlinear reaction--diffusion equation I: the case of small absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ezequiel Dratman","submitted_at":"2011-03-02T17:21:32Z","abstract_excerpt":"We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if \\emph{the absorption is small enough}, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the \"continuous\" equation. Furthermore, we exhibit an algorithm computing an $\\epsilon$-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is {\\em linear} in the numb"},"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":"1103.0491","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-03-02T17:21:32Z","cross_cats_sorted":[],"title_canon_sha256":"366eeb6a6abd1166e5bc1934d4f1827ecb13e95e66b2389e5df61b7447153fe0","abstract_canon_sha256":"5a3bf1ca2cef94c6be4c6642bef2008d7f1239063b5be4c0c451722a626ea0f5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:34.782182Z","signature_b64":"+xz3/Cp7Gwvkx5s0uu9cLfNa3spS962kZY5GmNbQZPxPhuFn3RTTfFxgt263F+ZM93SmYP6prJqzCsEz46A3BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df9da50b891f3781a50cc6c3097d35e9e2e03538be6dddf538728543c36219d1","last_reissued_at":"2026-05-18T04:27:34.781564Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:34.781564Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient approximation of the solution of certain nonlinear reaction--diffusion equation I: the case of small absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ezequiel Dratman","submitted_at":"2011-03-02T17:21:32Z","abstract_excerpt":"We study the positive stationary solutions of a standard finite-difference discretization of the semilinear heat equation with nonlinear Neumann boundary conditions. We prove that, if \\emph{the absorption is small enough}, compared with the flux in the boundary, there exists a unique solution of such a discretization, which approximates the unique positive stationary solution of the \"continuous\" equation. Furthermore, we exhibit an algorithm computing an $\\epsilon$-approximation of such a solution by means of a homotopy continuation method. The cost of our algorithm is {\\em linear} in the numb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0491","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":"1103.0491","created_at":"2026-05-18T04:27:34.781666+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.0491v1","created_at":"2026-05-18T04:27:34.781666+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0491","created_at":"2026-05-18T04:27:34.781666+00:00"},{"alias_kind":"pith_short_12","alias_value":"36O2KC4JD43Y","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"36O2KC4JD43YDJIM","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"36O2KC4J","created_at":"2026-05-18T12:26:18.847500+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/36O2KC4JD43YDJIMY3BQS7JV5H","json":"https://pith.science/pith/36O2KC4JD43YDJIMY3BQS7JV5H.json","graph_json":"https://pith.science/api/pith-number/36O2KC4JD43YDJIMY3BQS7JV5H/graph.json","events_json":"https://pith.science/api/pith-number/36O2KC4JD43YDJIMY3BQS7JV5H/events.json","paper":"https://pith.science/paper/36O2KC4J"},"agent_actions":{"view_html":"https://pith.science/pith/36O2KC4JD43YDJIMY3BQS7JV5H","download_json":"https://pith.science/pith/36O2KC4JD43YDJIMY3BQS7JV5H.json","view_paper":"https://pith.science/paper/36O2KC4J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.0491&json=true","fetch_graph":"https://pith.science/api/pith-number/36O2KC4JD43YDJIMY3BQS7JV5H/graph.json","fetch_events":"https://pith.science/api/pith-number/36O2KC4JD43YDJIMY3BQS7JV5H/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/36O2KC4JD43YDJIMY3BQS7JV5H/action/timestamp_anchor","attest_storage":"https://pith.science/pith/36O2KC4JD43YDJIMY3BQS7JV5H/action/storage_attestation","attest_author":"https://pith.science/pith/36O2KC4JD43YDJIMY3BQS7JV5H/action/author_attestation","sign_citation":"https://pith.science/pith/36O2KC4JD43YDJIMY3BQS7JV5H/action/citation_signature","submit_replication":"https://pith.science/pith/36O2KC4JD43YDJIMY3BQS7JV5H/action/replication_record"}},"created_at":"2026-05-18T04:27:34.781666+00:00","updated_at":"2026-05-18T04:27:34.781666+00:00"}