Dr Amin Farjudian
and
Dr Michal Konecny
Computer Science, Aston University
|
Date: 27th June 2008 (Friday) |
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Time: 15:00 - 16:00 |
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Venue: MB146 |
Abstract
We present an implementation of the domain-theoretic Picard method
for solving initial value problems (IVPs) introduced by Edalat and
Pattinson in 2004. Compared to Edalat and Pattinson's implementation,
our algorithm uses a more efficient arithmetic based on an arbitrary
precision floating-point library. Despite the additional
overestimations due to floating-point rounding, we obtain a similar
bound on the convergence rate of the produced approximations.
Moreover, our convergence analysis is detailed enough to allow a
static optimisation in the growth of the precision used in successive
Picard iterations. Such optimisation greatly improves the efficiency
of the solving process. Although a similar optimisation could be
performed dynamically without our analysis, a static one gives us a
significant advantage: we are able to predict the time it will take
the solver to obtain an approximation of a certain (arbitrarily high)
quality.
