Efficient implementation of Radau collocation methods

TL;DR

This paper presents an efficient implementation of Radau IIA Runge-Kutta methods for stiff ODE problems, using a low-rank formulation and splitting procedure that improves performance and convergence.

Contribution

It introduces a novel low-rank formulation and splitting approach for Radau IIA methods, enhancing computational efficiency and convergence analysis.

Findings

Splitting procedure exhibits linear convergence with excellent properties.

Numerical tests confirm improved performance.

Implementation reduces computational cost for stiff ODEs.

Abstract

In this paper we define an efficient implementation of Runge-Kutta methods of Radau IIA type, which are commonly used when solving stiff ODE-IVPs problems. The proposed implementation relies on an alternative low-rank formulation of the methods, for which a splitting procedure is easily defined. The linear convergence analysis of this splitting procedure exhibits excellent properties, which are confirmed by its performance on a few numerical tests.