{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EJ4MSLOMXYRJUJII4HCLPOBYH6","short_pith_number":"pith:EJ4MSLOM","schema_version":"1.0","canonical_sha256":"2278c92dccbe229a2508e1c4b7b8383faea68e3928312c8943545cc66ec66d0f","source":{"kind":"arxiv","id":"1807.03728","version":2},"attestation_state":"computed","paper":{"title":"A second-order asymptotic-preserving and positivity-preserving exponential Runge-Kutta method for a class of stiff kinetic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jingwei Hu, Ruiwen Shu","submitted_at":"2018-07-10T16:00:38Z","abstract_excerpt":"We introduce a second-order time discretization method for stiff kinetic equations. The method is asymptotic-preserving (AP) -- can capture the Euler limit without numerically resolving the small Knudsen number; and positivity-preserving -- can preserve the non-negativity of the solution which is a probability density function for arbitrary Knudsen numbers. The method is based on a new formulation of the exponential Runge-Kutta method and can be applied to a large class of stiff kinetic equations including the BGK equation (relaxation type), the Fokker-Planck equation (diffusion type), and eve"},"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":"1807.03728","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-10T16:00:38Z","cross_cats_sorted":[],"title_canon_sha256":"f7e9bf8723987493bb44adf03c1ca1071c1b763ab78de072e4ea0f8de2a157ef","abstract_canon_sha256":"c9c4c0c7c0eca5c6d6146337508a5d542f2ea1370d556e5977193bd1f4155593"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:19.129377Z","signature_b64":"5TaWnVfpjYjDPp/xflHLs9zwOwkOt2CcQvoaoa9wFasza072CCn05v5+CPr0uqERuUb41RrVxuqBR+Lb15RxCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2278c92dccbe229a2508e1c4b7b8383faea68e3928312c8943545cc66ec66d0f","last_reissued_at":"2026-05-17T23:58:19.128872Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:19.128872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A second-order asymptotic-preserving and positivity-preserving exponential Runge-Kutta method for a class of stiff kinetic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jingwei Hu, Ruiwen Shu","submitted_at":"2018-07-10T16:00:38Z","abstract_excerpt":"We introduce a second-order time discretization method for stiff kinetic equations. The method is asymptotic-preserving (AP) -- can capture the Euler limit without numerically resolving the small Knudsen number; and positivity-preserving -- can preserve the non-negativity of the solution which is a probability density function for arbitrary Knudsen numbers. The method is based on a new formulation of the exponential Runge-Kutta method and can be applied to a large class of stiff kinetic equations including the BGK equation (relaxation type), the Fokker-Planck equation (diffusion type), and eve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03728","kind":"arxiv","version":2},"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":"1807.03728","created_at":"2026-05-17T23:58:19.128955+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.03728v2","created_at":"2026-05-17T23:58:19.128955+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03728","created_at":"2026-05-17T23:58:19.128955+00:00"},{"alias_kind":"pith_short_12","alias_value":"EJ4MSLOMXYRJ","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EJ4MSLOMXYRJUJII","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EJ4MSLOM","created_at":"2026-05-18T12:32:22.470017+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/EJ4MSLOMXYRJUJII4HCLPOBYH6","json":"https://pith.science/pith/EJ4MSLOMXYRJUJII4HCLPOBYH6.json","graph_json":"https://pith.science/api/pith-number/EJ4MSLOMXYRJUJII4HCLPOBYH6/graph.json","events_json":"https://pith.science/api/pith-number/EJ4MSLOMXYRJUJII4HCLPOBYH6/events.json","paper":"https://pith.science/paper/EJ4MSLOM"},"agent_actions":{"view_html":"https://pith.science/pith/EJ4MSLOMXYRJUJII4HCLPOBYH6","download_json":"https://pith.science/pith/EJ4MSLOMXYRJUJII4HCLPOBYH6.json","view_paper":"https://pith.science/paper/EJ4MSLOM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.03728&json=true","fetch_graph":"https://pith.science/api/pith-number/EJ4MSLOMXYRJUJII4HCLPOBYH6/graph.json","fetch_events":"https://pith.science/api/pith-number/EJ4MSLOMXYRJUJII4HCLPOBYH6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EJ4MSLOMXYRJUJII4HCLPOBYH6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EJ4MSLOMXYRJUJII4HCLPOBYH6/action/storage_attestation","attest_author":"https://pith.science/pith/EJ4MSLOMXYRJUJII4HCLPOBYH6/action/author_attestation","sign_citation":"https://pith.science/pith/EJ4MSLOMXYRJUJII4HCLPOBYH6/action/citation_signature","submit_replication":"https://pith.science/pith/EJ4MSLOMXYRJUJII4HCLPOBYH6/action/replication_record"}},"created_at":"2026-05-17T23:58:19.128955+00:00","updated_at":"2026-05-17T23:58:19.128955+00:00"}