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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenMon, 11 Dec 2023 11:22:02 +0000Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations
https://resolver.caltech.edu/CaltechAUTHORS:20120627-134902327
Authors: Kloeden, P. E.; Lorenz, J.
Year: 1986
DOI: 10.1137/0723066
We consider a dynamical system described by a system of ordinary differential equations which possesses a compact attracting set Λ of arbitrary shape. Under the assumption of uniform asymptotic stability of Λ in the sense of Lyapunov, we show that discretized versions of the dynamical system involving one-step numerical methods have nearby attracting sets Λ(h), which are also uniformly asymptotically stable. Our proof uses the properties of a Lyapunov function which characterizes the stability of Λ.https://authors.library.caltech.edu/records/ynb5n-q0564On the Rate of Convergence of Viscosity Solutions for Boundary Value Problems
https://resolver.caltech.edu/CaltechAUTHORS:LORsiamjma87
Authors: Lorenz, Jens; Sanders, Richard
Year: 1987
DOI: 10.1137/0518024
A class of singularly perturbed boundary value problems is considered for viscosity tending to zero. From compactness arguments it is known that the solutions converge to a limit function characterized by an entropy inequality. We formulate an approximate entropy inequality (AEI) and use it to obtain the order of convergence. The AEI is also used to obtain the order of convergence for monotone difference schemes.https://authors.library.caltech.edu/records/sr4nq-2xr38A High-Order Method for Stiff Boundary Value Problems with Turning Points
https://resolver.caltech.edu/CaltechAUTHORS:20120626-164218625
Authors: Brown, David L.; Lorenz, Jens
Year: 1987
DOI: 10.1137/0908067
This paper describes some high-order collocation-like methods for the numerical solution of stiff boundary-value problems with turning points. The presentation concentrates on the implementation of these methods in conjunction with the implementation of the a priori mesh construction algorithm introduced by Kreiss, Nichols and Brown [SIAM J. Numer. Anal., 23 (1986), pp. 325–368] for such problems. Numerical examples are given showing the high accuracy which can be obtained in solving the boundary value problem for singularly perturbed ordinary differential equations with turning points.https://authors.library.caltech.edu/records/d6vgs-z6v37