134 citations · 770 across the 68 of their papers we have counts for
9 papers · 1 filter
Diffractons: solitary waves created by diffraction in periodic media
David I. Ketcheson, Manuel Quezada de Luna
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and…
On the absolute stability regions corresponding to partial sums of the exponential function
David Ketcheson, Tihamér A. Kocsis, Lajos Lóczi
Certain numerical methods for initial value problems have as stability function the nth partial sum of the exponential function. We study the stability region, i.e., the set in the…
Error Analysis of Explicit Partitioned Runge-Kutta Schemes for Conservation Laws
Willem Hundsdorfer, David I. Ketcheson, Igor Savostianov
An error analysis is presented for explicit partitioned Runge-Kutta methods and multirate methods applied to conservation laws. The interfaces, across which different methods or ti…
Two-dimensional wave propagation in layered periodic media
Manuel Quezada de Luna, David I. Ketcheson
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive eff…
Propagation of internal errors in explicit Runge--Kutta methods and internal stability of SSP and extrapolation methods
David I. Ketcheson, Lajos Lóczi, Matteo Parsani
In practical computation with Runge--Kutta methods, the stage equations are not satisfied exactly, due to roundoff errors, algebraic solver errors, and so forth. We show by example…
Strong Stability Preserving Multistep Runge-Kutta Methods
Christopher Bresten, Sigal Gottlieb, Zachary Grant +3
High-order spatial discretizations with strong stability properties (such as monotonicity) are desirable for the solution of hyperbolic PDEs. Methods may be compared in terms of th…
A comparison of high order explicit Runge-Kutta, extrapolation, and deferred correction methods in serial and parallel
David I. Ketcheson, Umair bin Waheed
We compare the three main types of high-order one-step initial value solvers: extrapolation, spectral deferred correction, and embedded Runge--Kutta pairs. We consider orders four…
Rational functions with maximal radius of absolute monotonicity
Lajos Loczi, David I. Ketcheson
We study the radius of absolute monotonicity R of rational functions with numerator and denominator of degree s that approximate the exponential function to order p. Such functions…
Spatially partitioned embedded Runge-Kutta methods
David I. Ketcheson, Colin B. Macdonald, Steven J. Ruuth
We study spatially partitioned embedded Runge--Kutta (SPERK) schemes for partial differential equations (PDEs), in which each of the component schemes is applied over a different p…