Publication Details
Optimum Integration Step
Mikulášek Karel, RNDr., Ph.D. (FEECS BUT)
Pospíšil Pavel, Ing. (DCSE FEECS BUT)
Homogenous Differential Equations, Multiple Arithmetic, Modern Taylor Series Method
The best-known and most accurate method of calculating a new value of a numerical solution of a differential equation is to construct the Taylor series. Modern Taylor Series Method has proved to be both very accurate and fast. It is based on a direct use of the Taylor series. The main idea behind the Modern Taylor Series Method is an automatic integration method order setting, i.e. using as many Taylor series terms for computing as needed to achieve the required accuracy. It is the aim of this paper to show the advantage of the method when multiple arithmetic is used. Two examples of homogenous differential equations are presented. The rather detailed analysis can be applied to further types of problems.
@INPROCEEDINGS{FITPUB6235,
author = "Milena Hanz\'{a}lkov\'{a} and Karel Mikul\'{a}\v{s}ek and Pavel Posp\'{i}\v{s}il",
title = "Optimum Integration Step",
pages = "258--262",
booktitle = "Proceedings of 31st Conference Modelling and System Simulation MOSIS'97",
year = 1997,
location = "Ostrava, CZ",
ISBN = "80-85988-16-X",
language = "english",
url = "https://www.fit.vut.cz/research/publication/6235"
}