134 citations · 770 across the 68 of their papers we have counts for
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A multiscale model for weakly nonlinear shallow water waves over periodic bathymetry
David I. Ketcheson, Lajos Lóczi, Giovanni Russo
We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are…
Explicit Runge Kutta Methods that Alleviate Order Reduction
Abhijit Biswas, David I. Ketcheson, Steven Roberts +2
Explicit Runge--Kutta (RK) methods are susceptible to a reduction in the observed order of convergence when applied to initial-boundary value problem with time-dependent boundary c…
Accurate Solution of the Nonlinear Schrödinger Equation via Conservative Multiple-Relaxation ImEx Methods
Abhijit Biswas, David I. Ketcheson
The nonlinear Schrödinger (NLS) equation possesses an infinite hierarchy of conserved densities and the numerical preservation of some of these quantities is critical for accurate…
A high-order finite volume method for Maxwell's equations in heterogeneous and time-varying media
Damian P. San Roman Alerigi, David I. Ketcheson, Boon S. Ooi
We develop a finite volume method for Maxwell's equations in materials whose electromagnetic properties vary in space and time. We investigate both conservative and non-conservativ…
Order conditions for Runge--Kutta-like methods with solution-dependent coefficients
Thomas Izgin, David I. Ketcheson, Andreas Meister
In recent years, many positivity-preserving schemes for initial value problems have been constructed by modifying a Runge--Kutta (RK) method by weighting the right-hand side of the…
Multiple-Relaxation Runge Kutta Methods for Conservative Dynamical Systems
Abhijit Biswas, David I. Ketcheson
We generalize the idea of relaxation time stepping methods in order to preserve multiple nonlinear conserved quantities of a dynamical system by projecting along directions defined…