134 citations · 770 across the 68 of their papers we have counts for
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Energy Stability of Explicit Runge-Kutta Methods for Non-autonomous or Nonlinear Problems
Hendrik Ranocha, David I. Ketcheson
Many important initial value problems have the property that energy is non-increasing in time. Energy stable methods, also referred to as strongly stable methods, guarantee the sam…
Effective Rankine-Hugoniot conditions for shock waves in periodic media
David I. Ketcheson, Manuel Quezada de Luna
Solutions of first-order nonlinear hyperbolic conservation laws typically develop shocks in finite time even with smooth initial conditions. However, in heterogeneous media with ra…
Solitary water waves created by variations in bathymetry
Manuel Quezada de Luna, David I. Ketcheson
We study the flow of water waves over bathymetry that varies periodically along one direction. We derive a linearized, homogenized model and show that the periodic bathymetry induc…
Relaxation Runge-Kutta Methods: Conservation and stability for Inner-Product Norms
David I. Ketcheson
We further develop a simple modification of Runge--Kutta methods that guarantees conservation or stability with respect to any inner-product norm. The modified methods can be expli…
Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations
Hendrik Ranocha, Mohammed Sayyari, Lisandro Dalcin +2
The framework of inner product norm preserving relaxation Runge-Kutta methods (David I. Ketcheson, \emph{Relaxation Runge-Kutta Methods: Conservation and Stability for Inner-Produc…
Shoaling on Steep Continental Slopes: Relating Transmission and Reflection Coefficients to Green's Law
Jithin D. George, David I. Ketcheson, Randall J. LeVeque
The propagation of long waves onto a continental shelf is of great interest in tsunami modeling and other applications where understanding the amplification of waves during shoalin…
A path integral method for solution of the wave equation with continuously-varying coefficients
Jithin D. George, David I. Ketcheson, Randall J. LeVeque
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which informati…