40 citations · 93 across the 16 of their papers we have counts for
7 papers · 1 filter
Symbolic Manipulation of Flows of Nonlinear Evolution Equations, with Application in the Analysis of Split-Step Time Integrators
Winfried Auzinger, Harald Hofstaetter, Othmar Koch
We describe a package realized in the Julia programming language which performs symbolic manipulations applied to nonlinear evolution equations, their flows, and commutators of suc…
Setup of Order Conditions for Splitting Methods
Winfried Auzinger, Wolfgang Herfort, Harald Hofstätter +1
This article is based on earlier papers where an approach based on Taylor expansion and the structure of its leading term as an element of a free Lie algebra was described for the…
Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime
Winfried Auzinger, Thomas Kassebacher, Othmar Koch +1
The error behavior of exponential operator splitting methods for nonlinear Schr{ö}dinger equations in the semiclassical regime is studied. For the Lie and Strang splitting methods,…
Pixel matrices: An elementary technique for solving nonlinear systems
David I. Spivak
A new technique for approximating the entire solution set for a nonlinear system of relations (nonlinear equations, inequalities, etc. involving algebraic, smooth, or even continuo…
The BCH-Formula and Order Conditions for Splitting Methods
Winfried Auzinger, Wolfgang Herfort, Othmar Koch +1
As an application of the BCH-formula, order conditions for splitting schemes are derived. The same conditions can be obtained by using non-commutative power series techniques and i…
Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes
Winfried Auzinger, Harald Hofstätter, David Ketcheson +1
We present a number of new contributions to the topic of constructing efficient higher-order splitting methods for the numerical integration of evolution equations. Particular sche…
Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions
Winfried Auzinger, Othmar Koch, Michael Quell
We assess the applicability and efficiency of time-adaptive high-order splitting methods applied for the numerical solution of (systems of) nonlinear parabolic problems under perio…