{"paper":{"title":"Comparison of five methods of computing the Dirichlet-Neumann operator for the water wave problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.NA","authors_text":"Jon Wilkening, Vishal Vasan","submitted_at":"2014-06-19T21:45:04Z","abstract_excerpt":"We compare the effectiveness of solving Dirichlet-Neumann problems via the Craig-Sulem (CS) expansion, the Ablowitz-Fokas-Musslimani (AFM) implicit formulation, the dual AFM formulation (AFM*), a boundary integral collocation method (BIM), and the transformed field expansion (TFE) method. The first three methods involve highly ill-conditioned intermediate calculations that we show can be overcome using multiple-precision arithmetic. The latter two methods avoid catastrophic cancellation of digits in intermediate results, and are much better suited to numerical computation.\n  For the Craig-Sule"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5226","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"}