Adams, E.; Ames, W. F.; Kuhn, W.; Rufeger, W.; Spreuer, H.: Computational Chaos May Be Due to a Single Local Error. J. of Computational Physics 104, 241-250, 1993. Home/Search Document Not in Database Summary Related Articles Check |
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Literature on Enclosure Methods and Related Topics - Gerd Bohlender (1996) (Correct)
.... Jan95, Kea96] differential equations function space problems [Kau83, Mir83, Kau84, Kau85, Kau85a, Goe85, Nic86, Kau87a, Kau89, Kru85, Ral85, Dob86, Dob87, Cor85, Cor87, Cor88, Ham87a, Loh84, Loh85, Loh87, Loh88, Loh89, Loh89a, Spr87, Ame86, Wei87, Wei88, Ada87, Ada87a, Ada90, Ada91a, Ada91b, Ada93c, Ruf93, Goe90, Plu90, Plu91, Plu91a, Wat92, Ker91, Kol91, Kol91a, Ste90, Chr92, Kir92, Dav76, Bau80, Man90, Ohs88, Cor92a, Dob93, Nak88, Nak89, Nak90, Kue90, Nak90a, Nak91, Nak91a, Nak91b, Nak91c, Nak92, Nak92a, Nak92b, Tsu92, Neh92, Ott92, Rih91, Rih92, Loh92, Dur93, Nak93, Kau93, Rih94, Plu92, ....
.... [Sau86, Teu92] engineering problems [Cor87, Ada87a, Ams88, Ada89b, Ada91, Sch89, Sch90b, Sch91, Sch93a, Ada93b, Hei94] control theory [Gro93, Wal92b] MHD flow [Kle93, Geo92] electrical engineering [Wol90c, Sch92, Sch93] geometry [Ott87, Ott88] vortex dynamics [Ely91] computational chaos [Ada93c] liquid crystals [Non96] mathematics (double bubbles) Has96] other [Kle90a] ffl Literature lists and additional information: interval methods [Gar85, Gar87, Nic88, Yak92a, Yak92b] automatic differentiation [Jue91, Bis92, Cor91a, Cor92] published earlier version of this list [Boh93c] ....
Adams, E.; Ames, W. F.; Kuhn, W.; Rufeger, W.; Spreuer, H.: Computational Chaos May Be Due to a Single Local Error. J. of Computational Physics 104, 241-250, 1993.
Guaranteed Error Bounds for Ordinary Differential Equations - Corliss (1994) (3 citations) (Correct)
....and we must continue debugging. That is, interval techniques can assist the development of reliable algorithms by making our mistakes painfully obvious. 2.2. 6 Prove existence of a periodic solution Of particular interest in the context of dynamical systems, interval techniques have been used (see [3, 4, 5]) to prove the existence of both stable and unstable periodic solutions of certain chaotic systems by showing that the Poincair e return map has a fixed point. Another application is to gear drive vibrations where Adams used enclosure algorithms followed to discover that the standard model in the ....
....system for oe = 10, r = 28, b = 8=3, and t 2 [0; 10] In spite of this rather gloomy situation, enclosure methods have proven their merit in the study of chaotic systems. For example, Adams and Kuhn have used enclosure methods to prove the existence and uniqueness of unstable periodic solutions [3, 4, 5]. Spreuer and Adams [58] have verified and enclosed a homoclinic orbit for the Lorenz system. The game is to see how large a value of t f we can reach before the enclosure method breaks down. 4 Tools Purposes of this section: Interval arithmetic computes guaranteed range bounds. There are a ....
E. Adams, W. Ames, W. K uhn, W. Rufeger, and H. Spreuer, Computational chaos may be due to a single local error, J. Comput. Phys., 104 (1993).
A Brief Survey of Issues Relating to the Reliability of Simulation .. - Hayes (Correct)
....Second, backward error analysis should never be offered as more than a partial justification: it is still necessary to show, for example, that errors in the force field do not seriously effect the quantities of interest. A very interesting, but overly pessimistic, paper is one by Adams et al. [2]. They note that a numerical solution to an ODE always remains close to a true solution of the problem for some length of time. The interesting quantity is the typical length scale of each of these sections of the numerical solution. This is similar to the idea of shadow segments discussed by ....
....discusses other measures of error that may be used if shadowing turns out to be too stringent a measure of error. Finally, there may be the possibility of proving rigorously that a shadow does not exist. The literature on this subject seems rather sparse; it is mentioned briefly in Adams et al. [2] and Iserles et al. 42] Glossary Like most groups of technical people, stellar dynamicists have a language all their own. This glossary is informal, and constitutes an exceedingly brief and fleeting crash course in stellar dynamics for those members of my committee not familiar with the terms. ....
E. Adams, W. F. Ames, W. Kuhn, W. Rufeger, and H. Spreuer. Computational chaos may be due to a single local error. Journal of Computational Physics, 104:241--250, 1993.
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