{"paper":{"title":"Filon-Clenshaw-Curtis rules for highly-oscillatory integrals with algebraic singularities and stationary points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"I. G. Graham, T. Kim, V. Dominguez","submitted_at":"2012-07-10T09:48:22Z","abstract_excerpt":"In this paper we propose and analyse composite Filon-Clenshaw-Curtis quadrature rules for integrals of the form $I_{k}^{[a,b]}(f,g) := \\int_a^b f(x) \\exp(\\mathrm{i}kg(x)) \\rd x $, where $k \\geq 0$, $f$ may have integrable singularities and $g$ may have stationary points. Our composite rule is defined on a mesh with $M$ subintervals and requires $MN+1$ evaluations of $f$. It satisfies an error estimate of the form $C_N k^{-r} M^{-N-1 + r}$, where $r$ is determined by the strength of any singularity in $f$ and the order of any stationary points in $g$ and $C_N$ is a constant which is independent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2283","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"}