Work

Adaptive time step selection for spectral deferred correction

Year: 2024

Type: article

Abstract: 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.

Source: Numerical Algorithms

DOI: 10.1007/s11075-024-01964-z

Authors: Thomas Saupe, Sebastian Götschel, Thibaut Lunet, Daniel Ruprecht, Robert Speck

Institutions: Forschungszentrum Jülich, Jülich Supercomputing Centre, Hamburg University of Technology

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: European Commission, Bundesministerium für Bildung und Forschung