{"paper":{"title":"Computation of some dispersive equations through their iterated linearisation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Arieh Iserles, Guannan Chen, Karolina Kropielnicka, Pranav Singh","submitted_at":"2024-05-08T10:55:47Z","abstract_excerpt":"It is often the case that, while the numerical solution of the non-linear dispersive equation $\\mathrm{i}\\partial_t u(t)=\\mathcal{H}(u(t),t)u(t)$ represents a formidable challenge, it is fairly easy and cheap to solve closely related linear equations of the form $\\mathrm{i}\\partial_t u(t)=\\mathcal{H}_1(t)u(t)+\\widetilde{\\mathcal H}_2(t)u(t)$, where $\\mathcal{H}_1(t)+\\mathcal{H}_2(v,t)=\\mathcal{H}(v,t)$. In that case we advocate an iterative linearisation procedure that involves fixed-point iteration of the latter equation to solve the former. A typical case is when the original problem is a no"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04958","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.04958/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}