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ODEs and redefining the concept of elementary functions. (English) Zbl 1052.34500

Sloot, Peter M. A. (ed.) et al., Computational science - ICCS 2002. 2nd international conference, Amsterdam, the Netherlands, April. 21–24, 2002. Proceedings. Part 1. Berlin: Springer (ISBN 3-540-43591-3). Lect. Notes Comput. Sci. 2329, 1000-1009 (2002).
Summary: The modern concept of elementary functions and the Taylor method are deeply connected. The article summarizes the remarkable (although not widely known) facts about the modern Taylor method, Ordinary Differential Equations (ODEs) and the modern notion of elementary functions – the property that actually takes place for all ODEs used in applications. Beside the typical usage of the Taylor method for integrating initial value problems, two new applications of the Taylor method are considered: integrating until the given end value of a dependent variable, and integrating the boundary value problem.
For the entire collection see [Zbl 0988.68835].

MSC:

34A45 Theoretical approximation of solutions to ordinary differential equations
34B99 Boundary value problems for ordinary differential equations

Software:

Taylor center
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