3 papers
math.AP2024
Existence of undercompressive travelling waves of a non-local generalised Korteweg-de Vries-Burgers equation
F. Achleitner, C. M. Cuesta, X. Diez-Izagirre
We study travelling wave solutions of a generalised Korteweg-de Vries-Burgers equation with a non-local diffusion term and a concave-convex flux. This model equation arises in the…
math.NA2023
Hypocoercivity for Linear ODEs and Strong Stability for Runge--Kutta Methods
Franz Achleitner, Anton Arnold, Ansgar Jüngel
In this note, we connect two different topics from linear algebra and numerical analysis: hypocoercivity of semi-dissipative matrices and strong stability for explicit Runge--Kutta…
math.NA2023
Necessary and sufficient conditions for strong stability of explicit Runge-Kutta methods
Franz Achleitner, Anton Arnold, Ansgar Jüngel
Strong stability is a property of time integration schemes for ODEs that preserve temporal monotonicity of solutions in arbitrary (inner product) norms. It is proved that explicit…