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Please use this identifier to cite or link to this item: http://tainguyenso.vnu.edu.vn/jspui/handle/123456789/6643

Title: Continuous variable stepsize explicit pseudo two-step RK methods
Authors: Cong, N.H.
Keywords: Embedded and dense output formulas
Parallelism
Runge-kutta methods
Two-step runge-kutta methods
Issue Date: 1999
Publisher: Journal of Computational and Applied Mathematics
Citation: Volume: 101 Issue: 2-Jan Page : 105-116
Abstract: The aim of this paper is to apply a class of constant stepsize explicit pseudo two-step Runge-Kutta methods of arbitrarily high order to nonstiff problems for systems of first-order differential equations with variable stepsize strategy. Embedded formulas are provided for giving a cheap error estimate used in stepsize control. Continuous approximation formulas are also considered for use in an eventual implementation of the methods with dense output. By a few widely used test problems, we compare the efficiency of two pseudo two-step Runge-Kutta methods of orders 5 and 8 with the codes DOPRI5, DOP853 and PIRK8. This comparison shows that in terms of f-evaluations on a parallel computer, these two pseudo two-step Runge-Kutta methods are a factor ranging from 3 to 8 cheaper than DOPRI5, DOP853 and PIRK8. Even in a sequential implementation mode, fifth-order new method beats DOPRI5 by a factor more than 1.5 with stringent error tolerances. ?? 1999 Elsevier Science B.V. All rights reserved.
URI: http://tainguyenso.vnu.edu.vn/jspui/handle/123456789/6643
ISSN: 3770427
Appears in Collections:To-2000 VNU-DOI-Publications

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