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Mathematics > Numerical Analysis

arXiv:2411.14399 (math)
[Submitted on 21 Nov 2024]

Title:DiscoTEX 1.0: Discontinuous collocation and implicit-turned-explicit (IMTEX) integration symplectic, symmetric numerical algorithms with high order jumps for differential equations II: extension to higher-orders of numerical convergence

Authors:Lidia J. Gomes Da Silva
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Abstract:\texttt{DiscoTEX} is a highly accurate numerical algorithm for computing numerical weak-form solutions to distributionally sourced partial differential equations (PDE)s. The aim of this second paper, succeeding \cite{da2024discotex}, is to present its extension up to twelve orders. This will be demonstrated by computing numerical weak-form solutions to the distributionally sourced wave equation and comparing it to its exact solutions. The full details of the numerical scheme at higher orders will be presented.
Comments: 15 pages, 5 figures, 2 tables. Second paper of a series of papers. See this http URL:2401.08758 for application of these algorithms to numerical black hole perturbation theory. Comments welcomed. arXiv admin note: text overlap with arXiv:2401.08758
Subjects: Numerical Analysis (math.NA); Instrumentation and Methods for Astrophysics (astro-ph.IM); General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph)
Cite as: arXiv:2411.14399 [math.NA]
  (or arXiv:2411.14399v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2411.14399

Submission history

From: Lidia J. Gomes Da Silva Miss [view email]
[v1] Thu, 21 Nov 2024 18:28:19 UTC (4,691 KB)
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