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Technical Initial Problems and Automatic Transformation

机译:技术性初始问题和自动转换

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In this paper an outline is given of historical and current developments in the application of recurrent Taylor series to the integration of systems of ordinary differential equations. Then an extremely accurate and fast method for the numerical solution of ordinary differential equations is presented. In general Taylor series method is not included or even mentioned in surveys on numerical integration techniques as the programs were written by mathematicians with the main objective of demonstrating the feasibility of the concept and with the goal of finding integration algorithms of very high accuracy. For this reason such programs should be looked upon as a stimulus for writing more advanced software employing Taylor series better able to compete with programs using other methods. An attempt in this direction is TKSL, a program the results of which will be dealt with.
机译:本文概述了递归泰勒级数在常微分方程组积分中的应用的历史和当前发展。然后提出了一种非常精确,快速的常微分方程数值解方法。通常,泰勒级数方法没有包括在数值积分技术的调查中,甚至没有提到,因为该程序是由数学家编写的,其主要目的是证明该概念的可行性,并且其目的是找到非常高精度的积分算法。因此,应将此类程序视为刺激因素,以编写使用Taylor系列的更高级软件,使其更能与使用其他方法的程序竞争。为此尝试了TKSL,该程序的结果将得到处理。

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