1 citations · 2 across the 5 of their papers we have counts for
11 papers
Projected Data Assimilation using Sliding Window Proper Orthogonal Decomposition
Aishah Albarakati, Marko Budisic, Erik Van Vleck
Prediction of the state evolution of complex high-dimensional nonlinear systems is challenging due to the nonlinear sensitivity of the evolution to small inaccuracies in the model.…
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…
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…