Abstract
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.
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© 2002 Springer-Verlag Berlin Heidelberg
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Gofen, A. (2002). ODEs and Redefining the Concept of Elementary Functions. In: Sloot, P.M.A., Hoekstra, A.G., Tan, C.J.K., Dongarra, J.J. (eds) Computational Science — ICCS 2002. ICCS 2002. Lecture Notes in Computer Science, vol 2329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46043-8_101
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DOI: https://doi.org/10.1007/3-540-46043-8_101
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