A high order, block finite difference, error inhibiting scheme for the transport equation

2024/02/18 by Adi Ditkowski, Ditkowski, Adi, Anne Le Blanc +3
Engineering · Mathematics · #65M06 #65M12 #65M15 #65M60 #Differential Equations and Numerical Methods #FOS: Mathematics #G.1.8 #Nuclear reactor physics and engineering #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2402.11617

openalex publication_date 2024/02/18 · openalex created_date 2024/02/22 · openalex updated_date 2026/07/28

Abstract

We propose a block finite difference, error inhibiting scheme that is fourth-order accurate for short to moderate times and has a six-order convergence rate for long times. This scheme outperforms the standard fourth-order Finite Difference scheme. We also demonstrate that the proposed scheme is a particular type of nodal-based Discontinuous Galerkin method with p=1.

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