2 papers
math.NA2020
Stability theory for some scalar finite difference schemes : Validity of the modified equations approach
Firas Dhaouadi, Emilie Duval, Sergey Tkachenko +1
In this paper, we discuss some limitations of the modified equations approach as a tool for stability analysis for a class of explicit linear schemes to scalar partial derivative e…
math-ph2019
Hyperbolicity of the modulation equations for the Serre-Green-Naghdi model
Sergey Tkachenko, Sergey Gavrilyuk, Keh-Ming Shyue
Serre-Green-Naghdi equations (SGN equations) is the most simple dispersive model of long water waves having "good" mathematical and physical properties. First, the model is a mathe…