{"paper":{"title":"Spectral parameter power series for polynomial pencils of Sturm-Liouville operators and Zakharov-Shabat systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NA"],"primary_cat":"math.CA","authors_text":"Sergii M. Torba, Ulises Velasco-Garcia, Vladislav V. Kravchenko","submitted_at":"2014-01-07T21:42:36Z","abstract_excerpt":"A spectral parameter power series (SPPS) representation for solutions of Sturm-Liouville equations of the form $$(pu')'+qu=u\\sum_{k=1}^{N}\\lambda^{k}r_{k}$$ is obtained. It allows one to write a general solution of the equation as a power series in terms of the spectral parameter $\\lambda$. The coefficients of the series are given in terms of recursive integrals involving a particular solution of the equation $(pu_{0}')'+qu_{0}=0$. The convenient form of the solution provides an efficient numerical method for solving corresponding initial value, boundary value and spectral problems.\n  A specia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1520","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"}