A MATLAB implementation of TASE-RK methods

Abstract

In this paper, we analyze theoretical and implementation aspects of Time-Accurate and highly-Stable Explicit Runge-Kutta (TASE-RK) methods, which have been recently introduced by Bassenne et al. (2021) [5], for the numerical solution of stiff Initial Value Problems (IVPs). These methods are obtained by combining explicit RK schemes with suitable matrix operators, called TASE operators, involving in their expression a matrix J related to the Jacobian of the differential problem to be solved. By analyzing the formulation and order conditions of TASE-RK methods, we show that they can be interpreted as particular linearly implicit RK schemes, and that their consistency properties are independent of the choice of J. Using this information, we propose a MATLAB implementation of TASE-RK methods, which makes use of matrix factorizations and allows setting J according to user preferences.