98 citations · 124 across the 9 of their papers we have counts for
11 papers
Convergence of the harmonic balance method for smooth Hilbert space valued differential-algebraic equations
Andrew Steyer, Robert J. Kuether
We analyze the convergence of the harmonic balance method for computing isolated periodic solutions of a large class of continuously differentiable Hilbert space valued differentia…
An energy consistent discretization of the nonhydrostatic equations in primitive variables
Mark A. Taylor, Oksana Guba, Andrew Steyer +3
We derive a formulation of the nonhydrostatic equations in spherical geometry with a Lorenz staggered vertical discretization. The combination conserves a discrete energy in exact…
Efficient IMEX Runge-Kutta methods for nonhydrostatic dynamics
Andrew Steyer, Christopher J. Vogl, Mark Taylor +1
We analyze the stability and accuracy (up to third order) of a new family of implicit-explicit Runge-Kutta (IMEX RK) methods. This analysis expedites development of methods with va…
Evaluation of Implicit-Explicit Additive Runge-Kutta Integrators for the HOMME-NH Dynamical Core
Christopher J. Vogl, Andrew Steyer, Daniel R. Reynolds +2
The nonhydrostatic High Order Method Modeling Environment (HOMME-NH) atmospheric dynamical core supports acoustic waves that propagate significantly faster than the advective wind…
Test equations and linear stability of implicit-explicit general linear methods
Andrew J. Steyer
Eigenvalue perturbation theory is applied to justify using complex-valued linear scalar test equations to characterize the stability of implicit-explicit general linear methods (IM…
Underlying one-step methods and nonautonomous stability of general linear methods
Andrew J. Steyer, Erik S. Van Vleck
We generalize the theory of underlying one-step methods to strictly stable general linear methods (GLMs) solving nonautonomous ordinary differential equations (ODEs) that satisfy a…
Projected Shadowing-based Data Assimilation
Bart de Leeuw, Svetlana Dubinkina, Jason Frank +3
In this article we develop algorithms for data assimilation based upon a computational time dependent stable/unstable splitting. Our particular method is based upon shadowing refin…
Detecting transient rate-tipping using Steklov averages and Lyapunov vectors
Alanna Hoyer-Leitzel, Alice Nadeau, Andrew Roberts +1
A wide variety of physical systems ranging from the firing of neurons to eutrophication of lakes to the presence of Arctic summer sea ice exhibit a phenomenon known as tipping. In…
Non-Autonomous Inertial Manifold Reduction
Yu-Min Chung, Andrew J. Steyer, Erik S. Van Vleck
Techniques are developed for decoupling dissipative differential equations. The approach considered is based upon obtaining a sufficient gap in the time dependent linear portion of…
Global Error Analysis and Inertial Manifold Reduction
Yu-Min Chung, Andrew Steyer, Michael Tubbs +2
Four types of global error for initial value problems are considered in a common framework. They include classical forward error analysis and shadowing error analysis together with…
A Lyapunov and Sacker-Sell spectral stability theory for one-step methods
Andrew J. Steyer, Erik S. Van Vleck
Approximation theory for Lyapunov and Sacker-Sell spectra based upon QR techniques is used to analyze the stability of a one-step method solving a time-dependent, linear, ordinary…