{"paper":{"title":"New, Highly Accurate Propagator for the Linear and Nonlinear Schr\\\"odinger Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","physics.chem-ph"],"primary_cat":"quant-ph","authors_text":"Hillel Tal-Ezer, Ido Schaefer, Ronnie Kosloff","submitted_at":"2012-04-17T11:33:38Z","abstract_excerpt":"A propagation method for the time dependent Schr\\\"odinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in system of ode's of the form u_t -Gu = s where G is a operator (matrix) and u is a time-dependent solution vector. Highly accurate methods, based on polynomial approximation of a modified exponential evolution operator, had been developed already for this type of problems where G is a linear, time independent matrix and s is a constant vector. In this paper we will describe a new algorit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3766","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"}