Time complexity and convergence analysis of domain theoretic Picard method

Farjudian, Amin and Konečný, Michal (2008). Time complexity and convergence analysis of domain theoretic Picard method. IN: Logic, language, information and computation. Hodges, Wilfrid and de Queiroz, Ruy (eds) Lecture notes in computer science . Berlin (DE): Springer.

Abstract

We present an implementation of the domain-theoretic Picard method for solving initial value problems (IVPs) introduced by Edalat and Pattinson [1]. 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.

Publication DOI: https://doi.org/10.1007/978-3-540-69937-8_14
Divisions: Engineering & Applied Sciences > Computer science
Engineering & Applied Sciences > Computer science research group
Additional Information: The original publication is available at www.springerlink.com
Full Text Link: http://www.spri ... 2778n2761v524u/
Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
Published Date: 2008
Authors: Farjudian, Amin
Konečný, Michal ( 0000-0003-2374-9017)

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