 A procedure with stepsize control for solving n one-dimensional IVPsDavod Khojasteh Salkuyeh, Faezeh Toutounian and Hamed Shariat Yazdi Mathematics and Computers in Simulation (MATCOM), 2008, vol. 79, issue 2, 167-176 Abstract: 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 library (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:79:y:2008:i:2:p:167-176 DOI: 10.1016/j.matcom.2007.11.004 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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