Singly Time–Accurate and highly–Stable Explicit (STASE)operators for the numerical solution of stiff differential equations

In this work, a new family of Time-Accurate and highly-Stable Explicit (TASE) operators for the numerical solution of stiff Initial Value Problems (IVPs) that extends that of M. Bassenne, L. Fu and A. Mani [Journal of Computational Physics 424 (2021): 109847] is proposed. The new TASE operators depend on the inverse of a single matrix (thus called Singly TASE — STASE operators), which are in contrast with Bassenne’s family that depends on $k$ different matrices to get order $k$. A complete study of A–stability properties is carried out for explicit Runge-Kutta (RK) schemes supplemented with STASE operators with order $k \le 4$. For orders two, three, and four, particular the schemes that are nearly strongly A–stable and therefore suitable for stiff problems are devised. A set of numerical experiments has been conducted to demonstrate the performance of the new methods by comparing them with previous RKTASE and other established methods.