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

TL;DR

DiscoTEX 1.0 is an advanced numerical algorithm designed for high-order solutions to distributionally sourced PDEs, extended to twelve orders, demonstrating improved accuracy in wave equation simulations.

Contribution

This paper extends DiscoTEX to higher orders up to twelve, providing detailed schemes and demonstrating its effectiveness on wave equations.

Findings

Achieved numerical solutions up to twelve orders of accuracy.

Validated the scheme against exact solutions of the wave equation.

Demonstrated high precision in distributionally sourced PDEs.

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.