{"paper":{"title":"A uniformly accurate (UA) multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Qinglin Tang, Weizhu Bao, Xiaowei Jia, Yongyong Cai","submitted_at":"2015-07-15T07:02:14Z","abstract_excerpt":"We propose and rigourously analyze a multiscale time integrator Fourier pseudospectral (MTI-FP) method for the Dirac equation with a dimensionless parameter $\\varepsilon\\in(0,1]$ which is inversely proportional to the speed of light. In the nonrelativistic limit regime, i.e. $0<\\varepsilon\\ll 1$, the solution exhibits highly oscillatory propagating waves with wavelength $O(\\varepsilon^2)$ and $O(1)$ in time and space, respectively. Due to the rapid temporal oscillation, it is quite challenging in designing and analyzing numerical methods with uniform error bounds in $\\varepsilon\\in(0,1]$. We p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04103","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"}