6 papers · 1 filter
Conserving mass, momentum, and energy for the Benjamin-Bona-Mahony, Korteweg-de Vries, and nonlinear Schrödinger equations
Hendrik Ranocha, David I. Ketcheson
We propose and study a class of arbitrarily high-order numerical discretizations that preserve multiple invariants and are essentially explicit (they do not require the solution of…
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 r…
Pseudo-Energy-Preserving Explicit Runge-Kutta Methods
Gabriel A. Barrios de León, David I. Ketcheson, Hendrik Ranocha
Using a recent characterization of energy-preserving B-series, we derive the explicit conditions on the coefficients of a Runge-Kutta method that ensure energy preservation (for Ha…
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…
A Comparative Study of Iterative Riemann Solvers for the Shallow Water and Euler Equations
Carlos Muñoz Moncayo, Manuel Quezada de Luna, David I. Ketcheson
The Riemann problem for first-order hyperbolic systems of partial differential equations is of fundamental importance for both theoretical and numerical purposes. Many approximate…