Adaptive time step selection for spectral deferred correction
Citation Link: https://doi.org/10.15480/882.13829
Publikationstyp
Journal Article
Date Issued
2024-10-28
Sprache
English
TORE-DOI
Journal
Volume
100
Issue
1
Start Page
369
End Page
393
Citation
Numerical Algorithms 100 (1): 369-393 (2025)
Publisher DOI
Scopus ID
Publisher
Springer
Spectral Deferred Correction (SDC) is an iterative method for the numerical solution of ordinary differential equations. It works by refining the numerical solution for an initial value problem by approximately solving differential equations for the error, and can be interpreted as a preconditioned fixed-point iteration for solving the fully implicit collocation problem. We adopt techniques from embedded Runge-Kutta Methods (RKM) to SDC in order to provide a mechanism for adaptive time step size selection and thus increase computational efficiency of SDC. We propose two SDC-specific estimates of the local error that are generic and do not rely on problem specific quantities. We demonstrate a gain in efficiency over standard SDC with fixed step size and compare efficiency favorably against state-of-the-art adaptive RKM.
Subjects
Adaptivity
Parallel-in-time
Spectral deferred correction
DDC Class
510: Mathematics
Publication version
publishedVersion