{"paper":{"title":"Efficient Numerical Method for Models Driven by L\\'evy Process via Hierarchical Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Eric Darve, Kailai Xu","submitted_at":"2018-12-18T02:35:19Z","abstract_excerpt":"Modeling via fractional partial differential equations or a L\\'evy process has been an active area of research and has many applications. However, the lack of efficient numerical computation methods for general nonlocal operators impedes people from adopting such modeling tools. We proposed an efficient solver for the convection-diffusion equation whose operator is the infinitesimal generator of a L\\'evy process based on $\\mathcal{H}$-matrix technique. The proposed Crank Nicolson scheme is unconditionally stable and has a theoretical $\\mathcal{O}(h^2+\\Delta t^2)$ convergence rate. The $\\mathca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.08324","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"}