2 citations · 3 across the 10 of their papers we have counts for
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Asymptotic-preserving and energy-conserving methods for a hyperbolic approximation of the BBM equation
Sebastian Bleecke, Abhijit Biswas, David I. Ketcheson +2
We study the hyperbolic approximation of the Benjamin-Bona-Mahony (BBM) equation proposed recently by Gavrilyuk and Shyue (2022). We develop asymptotic-preserving numerical methods…
High-order mass- and energy-conserving methods for the nonlinear Schrödinger equation and its hyperbolization
Hendrik Ranocha, David I. Ketcheson
We propose a class of numerical methods for the nonlinear Schrödinger (NLS) equation that conserves mass and energy, is of arbitrarily high-order accuracy in space and time, and re…
Maximum principle preserving space and time flux limiting for Diagonally Implicit Runge-Kutta discretizations of scalar convection-diffusion equations
Manuel Quezada de Luna, David I. Ketcheson
We provide a framework for high-order discretizations of nonlinear scalar convection-diffusion equations that satisfy a discrete maximum principle. The resulting schemes can have a…
Positivity preservation of implicit discretizations of the advection equation
Yiannis Hadjimichael, David I. Ketcheson, Lajos Lóczi
We analyze, from the viewpoint of positivity preservation, certain discretizations of a fundamental partial differential equation, the one-dimensional advection equation with perio…
On the Rate of Error Growth in Time for Numerical Solutions of Nonlinear Dispersive Wave Equations
Hendrik Ranocha, Manuel Quezada de Luna, David I. Ketcheson
We study the numerical error in solitary wave solutions of nonlinear dispersive wave equations. A number of existing results for discretizations of solitary wave solutions of parti…
A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations
Hendrik Ranocha, Dimitrios Mitsotakis, David I. Ketcheson
We develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta met…