Abstract The use of Artificial Neural Networks (ANNs) has spread massively in several
research fields. Among the various applications, ANNs have been exploited for the solution …

The paper is devoted to the parametric stability optimization of explicit Runge–Kutta
methods with higher-order derivatives. The key feature of these methods is the dependence …

Linearly implicit methods for Ordinary Differential Equations combined with the application of
Approximate Matrix Factorization (AMF) provide efficient numerical methods for the solution …

In this manuscript, we propose a new family of stabilized explicit parallelizable peer methods
for the solution of stiff Initial Value Problems (IVPs). These methods are derived through the …

This paper analyzes the stability of the class of time-accurate and highly-stable explicit
Runge–Kutta (TASE-RK) methods, introduced in 2021 by Bassenne, Fu, and Mani [J …

In this paper, the stability of θ-methods for delay differential equations is studied based on
the test equation y′(t)=− A y (t)+ B y (t− τ), where τ is a constant delay and A is a positive …

To improve the computational efficiency in implicit-explicit (IMEX) algorithms for stiff
detonation problems, the Mean Error Time Control (METC) method is proposed. The core of …

Singly-TASE operators for the numerical solution of stiff differential equations were proposed
by Calvo et al. in J. Sci. Comput. 2023 to reduce the computational cost of Runge–Kutta …

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 …

Mathematical models expressed through Partial Differential Equations (PDEs) represent
powerful a tool for the description and prediction of real phenomena in time and space. In …