Efficient implementation of Radau collocation methods
This work improves the computational efficiency of solving stiff ODEs, which is important for scientists and engineers in fields like chemical kinetics and fluid dynamics.
The paper presents an efficient implementation of Radau IIA Runge-Kutta methods for stiff ODE-IVPs using a low-rank formulation with a splitting procedure, demonstrating excellent linear convergence properties and performance on numerical tests.
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.