{"paper":{"title":"Finite difference method for a general fractional porous medium equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.NA","authors_text":"F\\'elix del Teso, Juan Luis V\\'azquez","submitted_at":"2013-07-09T14:33:31Z","abstract_excerpt":"We formulate a numerical method to solve the porous medium type equation with fractional diffusion \\[ \\frac{\\partial u}{\\partial t}+(-\\Delta)^{\\sigma/2} (u^m)=0 \\] posed for $x\\in \\mathbb{R}^N$, $t>0$, with $m\\geq 1$, $\\sigma \\in (0,2)$, and nonnegative initial data $u(x,0)$. We prove existence and uniqueness of the solution of the numerical method and also the convergence to the theoretical solution of the equation with an order depending on $\\sigma$. We also propose a two points approximation to a $\\sigma$-derivative with order $O(h^{2-\\sigma})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2474","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"}