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20192022
most citedExtended Lagrangian approach for the numerical study of multidimensional dispersive waves: applications to the Serre-Green-Naghdi equations

11 citations · 11 across the 2 of their papers we have counts for

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math.NA2022★ 11 cited

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…

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…