Giesl, Peter and McMichen, James (2018) Determination of the area of exponential attraction in one-dimensional finite-time systems using meshless collocation. Discrete and Continuous Dynamical Systems - Series B. ISSN 1531-3492
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Abstract
We consider a non-autonomous ordinary differential equation over a finite time interval [T1; T2]. The area of exponential attraction consists of solutions such that the distance to adjacent solutions exponentially contracts from T1 to T2. One can use a contraction metric to determine an area of exponential attraction and to provide a bound on the rate of attraction. In this paper, we will give the first method to algorithmically construct a contraction metric for finite-time systems in one spatial dimension. We will show the existence of a contraction metric, given by a function which satisfies a second-order partial differential equation with boundary conditions. We then use meshless collocation to approximately solve this equation, and show that the resulting approximation itself defines a contraction metric, if the collocation points are sufficiently dense. We give error estimates and apply the method to an example.
Item Type: | Article |
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Schools and Departments: | School of Mathematical and Physical Sciences > Physics and Astronomy |
Subjects: | Q Science > QA Mathematics |
Depositing User: | Billy Wichaidit |
Date Deposited: | 15 Nov 2017 10:11 |
Last Modified: | 16 Apr 2018 08:44 |
URI: | http://srodev.sussex.ac.uk/id/eprint/71249 |
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