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
arXiv:2411.14399
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.
15 pages, 5 figures, 2 tables. Second paper of a series of papers. See gr.qc:2401.08758 for application of these algorithms to numerical black hole perturbation theory. Comments welcomed. arXiv admin note: text overlap with arXiv:2401.08758