{"paper":{"title":"Comparison analysis on two numerical methods for fractional diffusion problems based on rational approximations of $t^{\\gamma}, \\ 0 \\le t \\le 1$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Joseph Pasciak, Pencho Marinov, Raytcho Lazarov, Stanislav Harizanov, Svetozar Margenov","submitted_at":"2018-05-02T10:25:59Z","abstract_excerpt":"We discuss, study, and compare experimentally three methods for solving the system of algebraic equations $\\mathbb{A}^\\alpha \\bf{u}=\\bf{f}$, $0< \\alpha <1$, where $\\mathbb{A}$ is a symmetric and positive definite matrix obtained from finite difference or finite element approximations of second order elliptic problems in $\\mathbb{R}^d$, $d=1,2,3$. The first method, introduced by Harizanov et.al, based on the best uniform rational approximation (BURA) $r_\\alpha(t)$ of $t^{1-\\alpha}$ for $0 \\le t \\le 1$, is used to get the rational approximation of $t^{-\\alpha}$ in the form $t^{-1}r_\\alpha(t)$. H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00711","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"}