Mathematics and computers in simulation, ( ISI ), Volume (79), Year (2008-11) , Pages (167-176)

Title : ( A procedure with stepsize control for solving n one-dimensional IVPs )

Authors: خجسته سالکویه , Faezeh Toutounian Mashhad , Hamed Shariat Yazdi ,

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Finite precision computations may affect the stability of algorithms and the accuracy of computed solutions. In this paper we first obtain a relation for computing the number of common significant digits between the exact solution and a computed solution of a one-dimensional initial-value problem obtained by using a single-step or multi-step method. In fact, by using the approximate solutions obtained with stepsizes h and h /2, the number of common significant digits between approximate solution with stepsize h and exact solution is estimated. Then by using the stochastic arithmetic, the CESTAC method, and the CADNA library we propose an algorithm to control the round-off error effect on the computed solution. This method can easily apply to a system of n one-dimensional initial-value problems. Finally some numerical examples are given to show the efficiency of the method.

Keywords

, Initial, value problem; Multi, step method; Single, step method; CESTAC method; CADNA
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@article{paperid:1009095,
author = {خجسته سالکویه and Toutounian Mashhad, Faezeh and Shariat Yazdi, Hamed},
title = {A procedure with stepsize control for solving n one-dimensional IVPs},
journal = {Mathematics and computers in simulation},
year = {2008},
volume = {79},
month = {November},
issn = {0378-4754},
pages = {167--176},
numpages = {9},
keywords = {Initial-value problem; Multi-step method; Single-step method; CESTAC method; CADNA library},
}

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%0 Journal Article
%T A procedure with stepsize control for solving n one-dimensional IVPs
%A خجسته سالکویه
%A Toutounian Mashhad, Faezeh
%A Shariat Yazdi, Hamed
%J Mathematics and computers in simulation
%@ 0378-4754
%D 2008

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