38 citations · 99 across the 16 of their papers we have counts for
4 papers · 1 filter
Uniform estimates for a fully discrete scheme integrating the linear heat equation on a bounded interval with pure Neumann boundary conditions
Guillaume Dujardin, Pauline Lafitte
This manuscript deals with the analysis of numerical methods for the full discretization (in time and space) of the linear heat equation with Neumann boundary conditions, and it pr…
Numerical computation of dark solitons of a nonlocal nonlinear Schrödinger equation
André de Laire, Guillaume Dujardin, Salvador López-Martínez
The existence and decay properties of dark solitons for a large class of nonlinear nonlocal Gross-Pitaevskii equations with nonzero boundary conditions in dimension one has been es…
Â-and Î-stability of collocation Runge-Kutta methods
Guillaume Dujardin, Ingrid Lacroix-Violet
This paper deals with stability of classical Runge-Kutta collocation methods. When such methods are embedded in linearly implicit methods as developed in [12] and used in [13] for…
High order linearly implicit methods for semilinear evolution PDEs
Guillaume Dujardin, Ingrid Lacroix-Violet
This paper considers the numerical integration of semilinear evolution PDEs using the high order linearly implicit methods developped in a previous paper in the ODE setting. These…