134 citations · 770 across the 68 of their papers we have counts for
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A conservative fully-discrete numerical method for the regularised shallow water wave equations
Dimitrios Mitsotakis, Hendrik Ranocha, David I. Ketcheson +1
The paper proposes a new, conservative fully-discrete scheme for the numerical solution of the regularised shallow water Boussinesq system of equations in the cases of periodic and…
Bound-preserving flux limiting for high-order explicit Runge-Kutta time discretizations of hyperbolic conservation laws
Dmitri Kuzmin, Manuel Quezada de Luna, David I. Ketcheson +1
We introduce a general framework for enforcing local or global maximum principles in high-order space-time discretizations of a scalar hyperbolic conservation law. We begin with su…
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…
Positivity-Preserving Adaptive Runge-Kutta Methods
Stephan Nüßlein, Hendrik Ranocha, David I Ketcheson
Many important differential equations model quantities whose value must remain positive or stay in some bounded interval. These bounds may not be preserved when the model is solved…
Optimal control of an SIR epidemic through finite-time non-pharmaceutical intervention
David I. Ketcheson
We consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reducti…
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…