A Convergence Theorem for the Parareal Algorithm Revisited

2024/05/11 by Scheiber, Ernest
#65L05 #65M22 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2405.06954

Abstract

The subject of the paper is to verify the convergence conditions for the parareal algorithm using Gander and Hairer's theorem . The analysis is conducted in the case where the coarse integrator is the Euler method and the high-accuracy integrator is an explicit Runge-Kutta type method.

Related

• Semi-explicit Parareal method based on convergence acceleration technique
• Robust Convergence of Parareal Algorithms with Arbitrarily High-order Fine Propagators
• On "Optimal" h-Independent Convergence of Parareal and MGRIT using Runge-Kutta Time Integration
• A Parareal algorithm without Coarse Propagator?
• Low-rank Parareal: a low-rank parallel-in-time integrator