11 citations · 11 across the 2 of their papers we have counts for
3 papers
Extended Lagrangian approach for the numerical study of multidimensional dispersive waves: applications to the Serre-Green-Naghdi equations
Sergey Tkachenko, Sergey Gavrilyuk, Jacques Massoni
In this paper we study two multidimensional nonlinear dispersive systems: the Serre-Green-Naghdi (SGN) equations describing dispersive shallow water flows, and Iordanskii-Kogarko-W…
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…
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…