01-422 A. Jorba, M. Zou

A software package for the numerical integration of ODE by means of high-order Taylor methods (781K, PostScript) Nov 14, 01

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Abstract. This paper revisits the Taylor method for the numerical integration of initial value problems of Ordinary Differential Equations (ODEs). The main issue is to present a computer program that, given a set of ODEs, produces the corresponding Taylor numerical integrator. The step size control adaptively selects both order and step size to achieve a prescribed error, and trying to minimize the global number of operations. The package provides support for several extended precision arithmetics, including user-defined types. The paper discusses the performance of the resulting integrator in some examples. As it can select the order of the approximation used, it has a very good behaviour for high accuracy computations. In fact, if we are interested in a very accurate computation in extended precision arithmetic, it becomes the best choice by far. The main drawback is that the Taylor method is an explicit method, so it has all the limitations of these kind of schemes. For instance, it is not suitable for stiff systems.

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