{"paper":{"title":"Modified Iterated Crank-Nicolson Method with Improved Accuracy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Jinjie Liu, Qiqi Tran","submitted_at":"2016-07-23T03:33:29Z","abstract_excerpt":"The iterated Crank-Nicolson (ICN) method is a successful numerical algorithm in numerical relativity for solving partial differential equations. The $\\theta$-ICN method is the extension of the original ICN method where $\\theta$ is the weight when averaging the predicted and corrected values. It has better stability when $\\theta$ is chosen to be larger than 0.5, but the accuracy is reduced since the $\\theta$-ICN method is second order accurate only when $\\theta$ = 0.5. In this paper, we propose two modified $\\theta$-ICN algorithms that have second order of convergence rate when $\\theta$ is not "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01344","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"}