{"paper":{"title":"New optimized Schwarz algorithms for one dimensional Schr\\\"odinger equation with general potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"BRGM), Coffee, F Xing (Jad","submitted_at":"2016-03-01T07:16:10Z","abstract_excerpt":"The aim of this paper is to develop new optimized Schwarz algorithms for the one dimensional Schr{\\\"o}dinger equation with linear or nonlinear potential. After presenting the classical algorithm which is an iterative process, we propose a new algorithm for the Schr{\\\"o}dinger equation with time-independent linear potential. Thanks to two main ingredients (constructing explicitly the interface problem and using a direct method on the interface problem), the new algorithm turns to be a direct process. Thus, it is free to choose the transmission condition. Concerning the case of time-dependent li"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00168","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"}