8 citations · 14 across the 12 of their papers we have counts for
16 papers
Operator splitting methods for non-autonomous evolution equations comprising three parts, with application to the Bloch-Torrey equation of MRI
Barbara Kaltenbacher, Pablo Muñoz, Mechthild Thalhammer
In this paper we devise and analyze Lie Trotter splitting schemes for non-autonomous evolution equations, following two approaches: 1) A fully non-autonomous scheme, motivated by t…
Convergence analysis of generalized modified splitting methods using multi-index series
Eugen Bronasco, Mechthild Thalhammer
We consider splitting methods for partial differential equations involving unbounded operators. For non-time-reversible dynamics, such as dissipative systems, negative splitting co…
Modified splitting methods for Gross-Pitaevskii systems modelling Bose-Einstein condensates: Time evolution and ground state computation
Mechthild Thalhammer, Gregor Thalhammer-Thurner
The year 2025 marks the 100 and 30 years anniversaries of the discovery of Bose--Einstein condensation and its successful experimental realisation. Inspired by these important rese…
Splitting methods with complex coefficients for linear and nonlinear evolution equations
Sergio Blanes, Fernando Casas, Cesareo Gonzalez +1
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achie…
Novel approaches for the reliable and efficient numerical evaluation of Landau-type operators
Jose Antonio Carrillo, Mechthild Thalhammer
Numerical approximations of Landau-type operators represent fundamental components of time integration methods for demanding problems such as inhomogeneous Vlasov-Landau-type equat…
Symmetric-conjugate splitting methods for evolution equations of parabolic type
Sergio Blanes, Fernando Casas, Cesáreo González +1
The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional bene…
Generalization of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type
Sergio Blanes, Fernando Casas, Cesáreo González +1
The present work is concerned with the extension of modified potential operator splitting methods to specific classes of nonlinear evolution equations. The considered partial diffe…
Community Integration Algorithms (CIAs) for Dynamical Systems on Networks
Tobias Böhle, Mechthild Thalhammer, Christian Kuehn
Dynamics of large-scale network processes underlies crucial phenomena ranging across all sciences. Forward simulation of large network models is often computationally prohibitive.…
On the reliable and efficient numerical integration of the Kuramoto model and related dynamical systems on graphs
Tobias Böhle, Christian Kuehn, Mechthild Thalhammer
In this work, a novel approach for the reliable and efficient numerical integration of the Kuramoto model on graphs is studied. For this purpose, the notion of order parameters is…
Efficient time integration methods for Gross--Pitaevskii equations with rotation term
Philipp Bader, Sergio Blanes, Fernando Casas +1
The objective of this work is the introduction and investigation of favourable time integration methods for the Gross--Pitaevskii equation with rotation term. Employing a reformula…
Splitting and composition methods with embedded error estimators
Sergio Blanes, Fernando Casas, Mechthild Thalhammer
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination…
Fundamental models in nonlinear acoustics part I. Analytical comparison
Barbara Kaltenbacher, Mechthild Thalhammer
This work is concerned with the study of fundamental models from nonlinear acoustics. In Part~I, a hierarchy of nonlinear damped wave equations arising in the description of sound…
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…
Efficient time integration methods based on operator splitting and application to the Westervelt equation
Barbara Kaltenbacher, Vanja Nikolic, Mechthild Thalhammer
Efficient time integration methods based on operator splitting are introduced for the Westervelt equation, a nonlinear damped wave equation that arises in nonlinear acoustics as ma…