Fixed Point Techniques in Analog Systems

Diogo Poças () and Jeffery Zucker ()
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Diogo Poças: McMaster University, Department of Mathematics and Statistics
Jeffery Zucker: McMaster University, Department of Mathematics and Statistics

A chapter in Mathematical and Computational Approaches in Advancing Modern Science and Engineering, 2016, pp 701-711 from Springer

Abstract: Abstract Analog computation is concerned with continuous rather than discrete spaces. Most of the physical processes arising in nature are modeled by differential equations, either ordinary (example: spring/mass/damper system) or partial (example: heat diffusion). In analog computability, the existence of an effective way to obtain solutions (either exact or approximate) of these systems is essential. We develop a framework in which the solutions can be seen as fixed points of certain operators on continuous data streams, using the framework of Fréchet spaces. We apply a fixed point construction to retrieve these solutions and present sufficient conditions on the operators and initial inputs to ensure existence and uniqueness of these corresponding fixed points.

Keywords: Fixed Point Technique; Parallel Systems; Present Sufficient Conditions; Parallel Computing; Time Evolution Problem (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-30379-6_63

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DOI: 10.1007/978-3-319-30379-6_63

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