{"paper":{"title":"Theory and internal structure of ADER-DG method for partial differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP","math.NA","physics.app-ph","physics.comp-ph"],"primary_cat":"physics.flu-dyn","authors_text":"I.S. Popov","submitted_at":"2026-06-14T06:00:07Z","abstract_excerpt":"Highly accurate stability boundary values for the ADER-DG method are obtained for arbitrary degrees $N$ of basis polynomials. In the linear case, stability is violated precisely when one of the matrix eigenvalues reaches $\\lambda = -1$, regardless of the phase $\\theta$. A rigorous mathematical framework for the stability is developed. The stability condition is significantly simplified, reducing it to the problem of calculating the roots of polynomials in the Courant number $\\mathrm{CFL}$. The maximum of the Courant numbers $\\mathrm{CFL}_{\\rm max}(N)$ are calculated. These results are new and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17100","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.17100/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}