422 citations · 2.4k across the 156 of their papers we have counts for
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Uncertainty quantification analysis of bifurcations of the Allen--Cahn equation with random coefficients
Christian Kuehn, Chiara Piazzola, Elisabeth Ullmann
In this work we consider the Allen--Cahn equation, a prototypical model problem in nonlinear dynamics that exhibits bifurcations corresponding to variations of a deterministic bifu…
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…
Continuation of Probability Density Functions using a Generalized Lyapunov Approach
S. Baars, J. P. Viebahn, T. E. Mulder +3
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational…
Combined Error Estimates for Local Fluctuations of SPDEs
Christian Kuehn, Patrick Kuerschner
In this work, we study the numerical approximation of local fluctuations of certain classes of parabolic stochastic partial differential equations (SPDEs). Our focus is on effects…
Analysis and numerics of traveling waves for asymmetric fractional reaction-diffusion equations
Franz Achleitner, Christian Kuehn
We consider a scalar reaction-diffusion equation in one spatial dimension with bistable nonlinearity and a nonlocal space-fractional diffusion operator of Riesz-Feller type. We pre…