TY  - JOUR
AU  - Baumann, Thomas
AU  - Götschel, Sebastian
AU  - Lunet, Thibaut
AU  - Ruprecht, Daniel
AU  - Speck, Robert
TI  - Adaptive time step selection for spectral deferred correction
JO  - Numerical algorithms
VL  - 100
SN  - 1017-1398
PB  - Springer Science  Business Media B.V.
M1  - FZJ-2024-07607
SP  - 369-393
PY  - 2025
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001344332600002
DO  - DOI:10.1007/s11075-024-01964-z
UR  - https://juser.fz-juelich.de/record/1034860
ER  -