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math.NA2012
Convergence of a fully discrete finite difference scheme for the Korteweg-de Vries equation
Helge Holden, Ujjwal Koley, Nils Henrik Risebro
We prove convergence of a fully discrete finite difference scheme for the Korteweg--de Vries equation. Both the decaying case on the full line and the periodic case are considered.…
math.NA2012
Operator splitting for well-posed active scalar equations
Helge Holden, Kenneth H. Karlsen, Trygve K. Karper
We analyze operator splitting methods applied to scalar equations with a nonlinear advection operator, and a linear (local or nonlocal) diffusion operator or a linear dispersion op…