6 citations · 14 across the 6 of their papers we have counts for
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An IMEX-RK scheme for capturing similarity solutions in the multidimensional Burgers' equation
Jens Rottmann-Matthes
In this paper we introduce a new, simple and efficient numerical scheme for the implementation of the freezing method for capturing similarity solutions in partial differential equ…
A splitting approach for freezing waves
Robin Flohr, Jens Rottmann-Matthes
We present a numerical method which is able to approximate traveling waves (e.g. viscous profiles) in systems with hyperbolic and parabolic parts by a direct long-time forward simu…
Freezing Traveling and Rotating Waves in Second Order Evolution Equations
Wolf-Jürgen Beyn, Denny Otten, Jens Rottmann-Matthes
In this paper we investigate the implementation of the so-called freezing method for second order wave equations in one and several space dimensions. The method converts the given…
Freezing similarity solutions in multi-dimensional Burgers' Equation
Jens Rottmann-Matthes
The topic of this paper are similarity solutions occurring in multi-dimensional Burgers' equation. We present a simple derivation of the symmetries appearing in a family of general…
Computation and Stability of Traveling Waves in Second Order Evolution Equations
Wolf-Jürgen Beyn, Denny Otten, Jens Rottmann-Matthes
The topic of this paper are nonlinear traveling waves occuring in a system of damped waves equations in one space variable. We extend the freezing method from first to second order…