Higher order operator splitting methods via Zassenhaus product formula: Theory and applications

Higher order operator splitting methods via Zassenhaus product formula: Theory and applications

In this paper, we contribute higher order operator-splitting method improved by Zassenhaus product. We apply the contribution to classical and iterative splitting methods. The underlying analysis to obtain higher order operator-splitting methods is presented. While applying the methods to partial differential equations, the benefits of balancing time and spatial scales are discussed to accelera...

Higher-order operator splitting methods for deterministic parabolic equations

Consistency of Iterative Operator-Splitting Methods: Theory and Applications

In this paper we describe a different operator-splitting method for decoupling complex equations with multi-dimensional and multiphysical processes for applications for porous media and phase-transitions. We introduce different operator-splitting methods with respect to their usability and applicability in computer codes. The error-analysis for the iterative operator-splitting methods is discus...

Weighted Iterative Operator-Splitting Methods and Applications

The subject of our research is to solve accurately ODEs, which appear in mathematical models arising from several physical processes. For this purpose we develop a new class of weighted iterative operator splitting methods. We present applications to systems of linear ODEs, which might contain also stiff parameters. The benefit of the proposed method is demonstrated with regard to convergence r...

Operator splitting and multigrid methods

In general we will be searching for methods of solving problems containing terms where the courant condition is too restrictive for practical computation; typical in this regard is the inclusion of diffusion or thermal conduction which contain second derivatives in space implying that time steps must scale as ∆t ∝ 1/(∆x). In this case we can not solve the problems explicitly but rather solve (a...