Butcher Series for the Convergence Analysis of Iterative Numerical Integrators: SDC and Parareal (Eugen Bronasco, Chalmers, Gothenburg)

02.12.2025 14:00

We present a Butcher series framework for analyzing the convergence of the Spectral Deferred Correction (SDC) and Parareal methods. SDC iteratively improves a low order approximation to achieve high order accuracy, while Parareal introduces parallelism in time by combining coarse and fine propagators. By expressing both algorithms as Runge-Kutta methods whose Butcher tableaus grow with each iteration, we apply classical Butcher series techniques to study their convergence. For SDC, we obtain convergence results under weaker assumptions, explain and exploit the order jump phenomenon, where the observed order of accuracy exceeds theoretical predictions, and design correctors that consistently produce it. For Parareal, we recover and refine known convergence results, offering problem agnostic insights into the structure of iterative time integration algorithms. This talk is based on joint work with Joscha Fregin (TUHH), Ausra Pogozelskyte, Daniel Ruprecht (TUHH), Gilles Vilmart (Univ. of Geneva).

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

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