{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2SHQVZKTAUGOVICOHPTEZSZRT4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a82b2e383d17c0516ddc082fcc2ef352cd00ff74fd2bc1bf12c64b5b925c39c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-05T09:49:09Z","title_canon_sha256":"30503ed59d963ebed17438b46fc0bb335f56eee61764c4cf9ef3638e8d2b99b2"},"schema_version":"1.0","source":{"id":"1604.01201","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.01201","created_at":"2026-05-18T01:05:12Z"},{"alias_kind":"arxiv_version","alias_value":"1604.01201v2","created_at":"2026-05-18T01:05:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01201","created_at":"2026-05-18T01:05:12Z"},{"alias_kind":"pith_short_12","alias_value":"2SHQVZKTAUGO","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"2SHQVZKTAUGOVICO","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"2SHQVZKT","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:1e840bf9d9bb83da84f164714decb2e0168d35dc085f9e0b74c70924ddc46adc","target":"graph","created_at":"2026-05-18T01:05:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under periodic boundary conditions. We discuss in particular several applications generating intricate patterns and displaying nonsmooth solution dynamics. First we give a general error analysis for splitting methods for parabolic problems under periodic boundary conditions and derive the necessary smoothness requirements on the exact solution in particular for the Gray-Scott equation and the Van der Pol equation. Numerical exa","authors_text":"Michael Quell, Othmar Koch, Winfried Auzinger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-05T09:49:09Z","title":"Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01201","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:33ed947a07e2c88aeebd98cdc0c18b9f59e7a125779058fe0db593948510466b","target":"record","created_at":"2026-05-18T01:05:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a82b2e383d17c0516ddc082fcc2ef352cd00ff74fd2bc1bf12c64b5b925c39c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-04-05T09:49:09Z","title_canon_sha256":"30503ed59d963ebed17438b46fc0bb335f56eee61764c4cf9ef3638e8d2b99b2"},"schema_version":"1.0","source":{"id":"1604.01201","kind":"arxiv","version":2}},"canonical_sha256":"d48f0ae553050ceaa04e3be64ccb319f06536d97a9b97ca61b6a7a21521f565d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d48f0ae553050ceaa04e3be64ccb319f06536d97a9b97ca61b6a7a21521f565d","first_computed_at":"2026-05-18T01:05:12.462194Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:12.462194Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"33lpHeH5gPtkbbVwjWTaVLjoUONTZiy9iA/++x/BSWbMTASkdzWxgI0aXRRX+C2wRwvGt4H4x7dWzQrxNhcKCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:12.462823Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.01201","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:33ed947a07e2c88aeebd98cdc0c18b9f59e7a125779058fe0db593948510466b","sha256:1e840bf9d9bb83da84f164714decb2e0168d35dc085f9e0b74c70924ddc46adc"],"state_sha256":"a5131d497661157eaab76dda87814b92a8ef07413d67d6341d083e9352cb1be0"}