This work explains how to solve evolution equations via novel iterative-based splitting
methods that efficiently use computational and memory resources. It focuses on systems of …

Decomposition, or splitting, finite difference methods have been playing an important role in
the numerical solution of nonsingular differential equation problems due to their remarkable …

In this paper we design higher-order time integrators for systems of stiff ordinary differential
equations. We combine implicit Runge–Kutta and BDF methods with iterative operator …

In this paper we give a short overview of some traditional operator splitting methods.
Furthermore, we introduce two recently developed methods, namely the additive splitting …

In this article, we consider iterative operator‐splitting methods for nonlinear differential
equations with bounded and unbounded operators. The main feature of the proposed idea …

In this paper, we propose a novel sequential data-driven method for dealing with equilibrium
based chemical simulations, which can be seen as a specific machine learning approach …

In this paper are presented some recent advances in multiscale splitting methods, based on
additive and iterative schemes and applied to deterministic and stochastic differential …

In this paper, a new numerical method is proposed and analyzed for the Allen–Cahn (AC)
equation. We divide the AC equation into linear section and nonlinear section based on the …

As an alternative to the classical splitting methods, two new splitting schemes have been
developed recently: the additive and the iterative splitting. In this paper we discuss the most …

This study was suggested by previous work on the simulation of evolution equations with
scale-dependent processes, eg, wave-propagation or heat-transfer, that are modeled by …