Please use this identifier to cite or link to this item: http://repository.vnu.edu.vn/handle/VNU_123/32316
Title: Continuous variable stepsize explicit pseudo two-step RK methods
Authors: NGUYEN, HUU CONG
Keywords: Runge-Kutta methods;Parallelism;Embedded and dense output formulas;Two-step Runge-Kutta-Nystrom methods
Issue Date: 1999
Publisher: ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Citation: ISIKNOWLEDGE
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 off-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. (C) 1999 Elsevier Science B.V. All rights reserved.
Description: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 101 Issue: 1-2 Pages: 105-116 ; TNS06669
URI: http://repository.vnu.edu.vn/handle/VNU_123/32316
ISSN: 0377-0427
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