A note on the stability of time–accurate and highly–stable explicit operators for stiff differential equations
M. Calvo, J.I. Montijano, L. Rández
Abstract
A family of Time-Accurate and highly-Stable Explicit (TASE) operators for the numerical solution of stiff IVPs that includes those proposed by Bassenne et al. (2021) [1] is proposed. In this family the TASE operator of order k depends on k free parameters in contrast with Bassenne's family in which it depends only on one parameter to be chosen for stability and accuracy requirements. A complete study of A–stability properties is carried out for explicit RK schemes supplemented with TASE operators with order k≤4. For orders 2, 3 and 4, particular schemes that are nearly strongly A–stable and therefore suitable for stiff problems are given. Some numerical experiments showing the behaviour of the methods are presented.