2 citations · 2 across the 2 of their papers we have counts for
13 papers
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…
General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes
Hendrik Ranocha, Lajos Lóczi, David I. Ketcheson
Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge-K…
Relaxation Runge-Kutta Methods for Hamiltonian Problems
Hendrik Ranocha, David I. Ketcheson
The recently-introduced relaxation approach for Runge-Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior o…